I also agree with the earlier commentator who said that you all were overthinking this.
His suggestion was that Reagan nominate a paleoconservative as his VP, who then succeeds Reagan. That is close, but I have a simpler suggestion.
My suggestion is that Ronald Reagan himself is your paleoconservative President. He did have paleoconservative types in his administration, most notably Pat Buchanan himself. No other late 20th/ early 21st President has done this, including Donald Trump (pretty much all the paleoconservatives in the Trump Adminstration were gone after a few months).
In this scenario, Reagan still does not have GHW Bush as his VP. This is because with Bush came alot of establishment Republicans filling high positions in the administration, most notably James Baker who definitely would not be there if Bush wasn't there. In this scenario, Bush doesn't win Iowa and exits the race as an also-ran early.
IOTL, Reagan dominated the 1980 Republican primaries, and Bush was the only other candidate to get any traction against Reagan, by winning six contests. Reagan got almost 60% of the total votes and Bush something like 23.6%. There are two ways you can go with this. Have Reagan be even more dominant and win all the states, in which case he has no need to reach out to the globalist/ internationalist/ establishment wing of the GOP and has more of a free hand in selecting his running mate and staffing his administration.
There is an alternative scenario that could work in that the runnner up in the 1980 Republican primaries is a pol somewhat less aligned with globalism than Bush, with Dole and Connally being the best president (there are no high profile paleocon politicians, but from a paleocon perspective either Dole or Connally are better than any of the Bushes, McCain, or Romney). Maybe Connally becomes Reagan's VP and Dole winds up in the administration as Secretary of State instead of Haig/ Schultz.
Both scenarios presume that Reagan himself is more sympathetic to paleoconservatism than he really was, so lets go with that.
So that is the AHC. Make Ronald Reagan more of a paleoconservative, and he doesn't have to compromise as much with the internationalist wing of the GOP because he either completely dominates the nomination process or the runner-up is less of an internationalist than Bush. At the least this pushes the Bushes into obscurity -they disappear into the corporate sector- so both Bush administrations are butterflied away and there is a good chance the Clinton administration gets butterflied away as well.