You’ve got it backwards. Democrats in “Democrat edge” states in the Northeast are even more to the left than usual, and nominal Republicans are closer to average Democrats in other parts of the country.
He’s not even a nominal Republican.
We have a precedent.
The first Republican President picked a border-state Democrat as his running mate to "unify the country."
A month into his term, a Democrat murdered him. His "unifying" VP became President and was an unreconstituted racist and a disaster. No thanks.
Trump has to pick a running mate of absolutely impeccable, genuine, conservative credentials, not only because of the state of the country and Trump's own doubtful history, but because of the very real possibility that -- God forbid, but we have to face it -- the tribalist party will try to take him out.
What you miss is that most Democrats & Republicans are not really ideological. Those that are draw the attention, and give those on other sides something to focus on, and to get excited over. But over the past two hundred years, the sustaining motivators for Party identifications, have been at least as functionally based on social identification as on ideological identification.