A second assumption is that parties don't reinvent themselves. Of course they do; if they're to last they have to reinvent themselves every generation or two. Go back through the history of both parties since the 1850s; ideological continuity in both cases is a fiction that papers over a series of opportunistic shifts in focus.
An empty shell of a party in a two-party system is like the shell of an abandoned building in Manhattan; the real estate is too valuable to remain unoccupied. So some time in the next twenty years as its demographics becomes untenable the Republican party will radically shift focus, with some kind of face-saving formulation that presents the fiction of continuity, or even a return to longstanding principles. This is just like the post-Reagan rightward shift in the Democratic party as the DLC became dominant in national Democratic politics. The old style social democratic (using European terminology) FDR Democrats remained with the party because they had no place else to go in a two party system.
Likewise the rump of the current social conservative and Evangelical Republican party will be made a welcome but impotent minority in the new Republican party. They'll get occasional lip service at in-party functions but they won't be allowed near the mic lest they spout what sounds like grandpa's crazy talk -- pretty much like the FDR style Democrats were treated by their party in the 90s and 00s.