This becomes much less of an issue if you close the primaries. Allowing independents or crossover voters to chose your candidate is about as smart as shipping a million U.S. ballots to China and asking them to fill them out. Dilute the conservative votes, get diluted candidates.
They won’t close the primaries, though. Now what?
Fundamentally, the Republican Party is an open political association.
If you live next to a slum and you put a big sign in front of your house that says “anyone who wants to can live here,” how long do you think you’re going to be able to endure living in your own house?
The problem is intrinsic.