Let's discuss the one-person, one-vote principle of Constitutional law, all of which has arisen in the context of Congressional districting.  
I.  The Equal Population Principle of One-Person, One-Vote
In Wesberry v. Sanders, 376 U.S. 1 (1964), the Supreme Court said that "as nearly as is practicable one man's vote in a congressional election is to be worth as much as another's.  This rule is followed automatically, of course, when Representatives are chosen as a group on a statewide basis, as was a widespread practice in the first 50 years of our Nation's history."   In Reynolds v. Sims, 377 U.S. 533 (1964), the Court explained that this principle was required by the Equal Protection Clause of the Fourteenth Amendment, and that "[d]iluting the weight of votes because of place of residence impairs basic constitutional rights under the Fourteenth Amendment just as much as invidious discriminations based upon factors such as race."  
Under these laws, one-person, one vote requires that single-member districts be substantially equal in population.  That is not a problem for the Virginia, Pennsylvania, etc., plans here, since each Congressional district has the same amount of voters in it.  But one-person, one-vote requires more.
II.  The Anti-Dilution and Anti-Discrimination Principles of One-Person, One-Vote
While these cases involved Congressional districts with unequal numbers of voters in them, the Court made clear that the one-person, one-vote standard was not limited to requiring equally-sized districts.  It also applied to the shape of voting districts.  In Gomillion v. Lightfoot, 364 US 339 (1960), the city of Tuskegee, Alabama redrew its shape from that of a square to an "uncouth twenty-eight sided figure," with the effect of "remov[ing] from the city all save only four or five of its 400 [African-American] voters while not removing a single white voter or resident."  The Court found that the petitioners could challenge this system as a violation of equal protection, and that "[a] statute which is alleged to have worked unconstitutional deprivations of petitioners' rights is not immune to attack simply because the mechanism employed by the legislature is a redefinition of municipal boundaries."
In cases not involving race, the Supreme Court likewise continued to suggest that political gerrymandering could violate Equal Protection.  In Gaffney v. Cummings, 412 U.S. 735, the Court noted that "districts may be equal or substantially equal in population and still be vulnerable under the Fourteenth Amendment," including districting plans "perfectly acceptable under equal population standards, but invidiously discriminatory because they are employed "to minimize or cancel out the voting strength of racial or political elements of the voting population."
Then, in Karcher v. Daggett, 462 U.S. 725 (1980), the Supreme Court invalidated New Jersey's new congressional districts.  Four votes were based solely on the equal-population principle, but Justice Stevens, who concurred and provided the fifth vote for invalidation, explained that he was also considering political gerrymandering.  Analyzing prior precedents, Justice Stevens explained that
political gerrymandering is one species of 'vote dilution' that is proscribed by the Equal Protection Clause," and concluded that "[t]he Equal Protection Clause requires every State to govern impartially. When a State adopts rules governing its election machinery or defining electoral boundaries, those rules must serve the interests of the entire community.  If they serve no purpose other than to favor one segment — whether racial, ethnic, religious, economic, or political — that may occupy a position of strength at a particular point in time, or to disadvantage a politically weak segment of the community, they violate the constitutional guarantee of equal protection.
 The four dissenters likewise correctly anticipated that "with ever more sophisticated computers, legislators can draw countless plans for absolute population equality," and then use that "equality" in order to discriminate politically: "[e]ven more than in the past, district lines are likely to be drawn to maximize the political advantage of the party temporarily dominant in public affairs."
III. The Dilution Principle in Political Gerrymandering: Justiciability Issues
In Davis v. Bandemer, 478 U.S. 109 (1986), a six-justice majority agreed that the Supreme Court could hear and resolve issues of political gerrymandering as a violation of equal protection.  There, Indiana's Republican-dominated legislature and governor passed a redistricting plan that contained a "political gerrymander intended to disadvantage Democrats."  In the first election with the new lines, Democrats won 51.9% of the state-wide Congressional vote but only 43% of the legislative seats.  But while the Court found it had the power to resolve the case, a majority found the gerrymander constitutional.  The largest plurality on the Court (four liberal justices) held that:
where unconstitutional vote dilution is alleged in the form of statewide political gerrymandering, the mere lack of proportional representation will not be sufficient to prove unconstitutional discrimination. Again, without specific supporting evidence, a court cannot presume in such a case that those who are elected will disregard the disproportionately underrepresented group. Rather, unconstitutional discrimination occurs only when the electoral system is arranged in a manner that will consistently degrade a voter's or a group of voters' influence on the political process as a whole.
Two other justices (including Justice Stevens) agreed that vote dilution stated an equal protection violation, but disagreed with the plurality's approach as to how such a claim would be proved.  It believed that a challenger had to address "shapes of voting districts and adherence to established political subdivision boundaries," and "the nature of the legislative procedures by which the apportionment law was adopted and legislative history reflecting contemporaneous legislative goals."
After more than a decade of partisan gerrymander claims, the Supreme Court essentially threw up its hands, on grounds of justiciability (the power of the Court to adequately fashion a remedy for the alleged violation.)  In Vieth v. Jubelirer, 541 U.S. 267 (2004), the entire court--even the conservatives--agreed that “partisan gerrymanders [are incompatible] with democratic principles.”  But a conservative plurality of four justices found that political gerrymandering issues were never justiciable, because there was no way for a court to determine what a constitutionally-required "fair" single-member district would look like, among other things.  
Justice Kennedy was the fifth vote to uphold the Pennsylvania gerrymander.  But he disagreed with the majority that political gerrymanders could NEVER be heard in federal court.  The four liberals at the time agreed with that.  (It was Stevens, Souter, Breyer, and Ginsberg.)  On the merits, Kennedy suggested that that political gerrymandering would violate EP if the law used "though generally permissible [political line drawing], were applied in an invidious manner or in a way unrelated to any legitimate legislative objective."  Kennedy also suggested that victims of political gerrymandering might have a First Amendment challenge.  
The liberal justices all agreed that political gerrymandering could state an equal protection violation, under somewhat different rationales.  Justice Stevens said that when "partisanship is the legislature's sole motivation — when any pretense of neutrality is forsaken unabashedly and all traditional districting criteria are subverted for partisan advantage — the governing body cannot be said to have acted impartially."  Breyer stated that "use of purely political boundary-drawing factors can amount to a serious, and remediable, abuse, namely the unjustified use of political factors to entrench a minority in power."  Justice Souter and Ginsburg laid out a complicated 5-part test, designed to determine whether a district was drawn sufficiently "unfairly" for a person in that district to have his vote matter.
IV.  Applying this law to the Republican Electoral College Schemes
Under these precedents, I believe that any Democratic voter of a state would have a strong equal protection challenge to the Republican scheme.  On the merits, there can be little doubt--indeed, it is all but admitted--that Republicans wish to change the way their states' electoral votes for purely political reasons, if not coded racial reasons.  ("Rural" voters, indeed.)  Given the facts on the ground, any of the various Vieth tests could arguably be satisfied here.  Republicans are attempting to "entrench a minority in power," to "unfairly" prevent states with a clear Democratic majority from electing a Democratic president, and using districts created for legislative purposes for an ulterior motive: to manipulate the vote for President.  Indeed, this added "twist" is something not seen in the redistricting cases: artificially-drawn legislative districts are not just being used to deny residents of those districts of the right to have a fair opportunity at electing their own representatives; these laws make sure that the political minority statewide can adversely affect the statewide majority from electing its preferred candidate.  In other words, this scheme will "consistently degrade a voter's or a group of voters' influence on the political process as a whole."  A majority of democrats statewide will cast 55% of the vote for Hilary Clinton, and give her maybe 20% of the state's electoral votes.  Republican's votes will be vastly more influential under this plan.  That is statewide vote dilution, anti-democratic, unequal, and unconstitutional.
Moreover, there is no justiciability problem here.  The Court will not need to get involved in drawing new, "fair" borders for Congressional districts.  Merely striking the new law down as unconstitutional, and returning to the old system of awarding electoral votes to the state-wide winner, would be a complete remedy that is plainly consistent with one-person, one-vote standard.  This is the purest democratic principle: he or she with the most votes wins.
Anyway, these are just my thoughts after a few hours.  But do not simply acquiesce when you hear someone say that the Republican electoral-vote rigging scheme is constitutional.  It is not.  And it will be challenged in the Courts if it passes.  And there may be five votes already--more, if God willing, some of the conservative justices find themselves off the bench.