what if Republicans went back to being the coastal elitist, hawkish, socially liberal Ayn-Rand lovers that we used to be? Would that be FF or HP?
It'd be just as HP and the current GOP and just as HP as the Reagan/Gingrich/Bush era GOP was (not that there's much difference between the two). I'd like the GOP to become the party of Ike and Rockefeller again, and they weren't Ayn Rand lovers by any stretch. Ike also couldn't be considered a "Coastal Elitist." I don't think the types of Republicans you describe ever existed, or at the very least had any kind of power/influence over the party. There were Coastal Elites, there were/are hawks, and there were Social Libertarians, but there weren't any Republicans that carried all those traits.
Immigration is the big difference
IKE and Rockefeller if the were politicians today would be much more conservative than they were then and would basically be like John McCain or Mitt Romney
Immigration aside, in IKE's case anyway, they'd be more McCain than Romney. There's key differences even between those two.
I would say
Eisenhower would be like McCain
Rockefeller is like Romney in ways that both really dont care about social issues or most issues outside economics. Rockefeller was the establishment candidate in the era which was dominated by the Keynesian Consensus while Romney was in the era dominated by Neo-Liberalism but other than that they are very similar