I can see Asians voting atleast 40-45% Republican if the Republicans become more friendly to non-whites. They voted Republican until the 90s, and since they're even wealthier than whites as a group the GOP should atleast try to make the Asian vote competitive. Hispanics should be harder, but the Republicans still should be able to get more than the anemic 27/29% Romney and Trump got if they try.
There are plenty of wealthy and/or socially conservative Hispanics who didn't want to vote for Trump or Romney (remember the "self-deportation" gaffe). I don't see any Republican getting more than 12% with African Americans in the foreseeable future.
The problem is that making inroads with minorities probably will cost the GOP votes with non college-educated whites (and probably some college-educated whites as well). Personally I'd trade off some whites for affluent and/or conservative minorities as a whites-only GOP isn't viable on the long term (and sucks ideologically), but we shouldn't forget that the EC heavily favours people using Trump's strategy (Asians and Latino's live in non-competititve states).
The Asian American population was predominantly christian in that era, newer Asian-American immigrants have a higher percentage of non-Christians. They don't like the christian right. As you mention in your last paragraph, outreach to certain demographics will have implications on other demographics. Trying to appeal to Asian-Americans would weaken GOP support amongst Religious Christians.
