Maybe it's not just about the votes?

Maybe what we're observing, with left-wing capture of most institutions despite roughly half the country voting Republican, is the limits of focusing on just capturing enough votes to narrowly win elections, as per conventional political theory. Maybe a party has to also win hearts and minds of a significant enough fraction of elites if not even wider professional class to be a viable force in society. Else you can't be effective even if you're in office - or rather, as with Trump, end up implementing largely your party's professional/elite voters view rather than majority of voters' (eg, no wall but corp tax cuts). More fundamentally, legislation wouldn't fly if it doesn't have legs - it only works well if it caps and reinforces changes already underway in the society - meaning, already being widely spread and promoted by a non-trivial fraction of elite and professionals. And if all legs are turning left not much can be saved by legislating the right turn.

I don't think elites and professionals being so left-wing is inevitable. If anything, engineers, economists, financiers would've likely been right of center on average half a century ago. But it certainly seems that the way current political coalition cuts is that republicans end up with severely insufficient support among elites and top professionals. They would need to focus on this and change it if they are to recover as a productive force. And this is a rather separate goal from just capturing a bit more Hispanic lower class vote which is the most immediate strategy for winning the next election.