Maxwell, who was the last republican that won an election?
George W. Bush, the establishments choice, who ran as a certifiable Rockefeller Republican, according to Limbaugh, for as long as he could in the 2000 Presidential Election until it was realized his main opponent for the nomination was John McCain. His general election campaign was fairly moderate by modern Republican standards as well. In 2004 he shifted right but even then he had massive leverage and he obviously wasn't any of the names I mentioned.
Plus, don't you conservatives recoil at his memory at this point?
Yes, Bush was a "conservative who ran as a moderate". That is, the Republican base believed that he was one of them (in part because of the primary campaign against McCain, but also for reasons of cultural identification). And so, since he had the base in his pocket, Bush was free to spend the general election campaign talking about things like education, a Medicare prescription drug benefit, etc. It was a campaign that allowed him to reach out to the center. Contrast that with McCain and Romney, who in subsequent contests had the image of a "moderate", and so had to be "moderates who ran as conservatives". That is, they had to spend way too much time sucking up to the conservative base, because the conservative base didn't believe they were really conservative.
A "conservative who runs as a moderate" seems like the smarter way to go, assuming you can find someone who can pull it off.