They never converted to "actual conservatism." They converted actual conservatism to welfare-state liberalism, by making New Deal and later Great Society policies mainstream rather than anathema in the Republican Party. These are the same people that tell us how we're supposed revere Martin Luther King as some kind of conservative hero, after all.
At no time was it imaginable that conservatism could be confused with pacifist weenieism which was the dead hand of a dead "conservatism" of the 1930s: Lindbergh, Colonel McCormick, "America First" and admiration for the likes of Neville Chamberlain. I would imagine that the "paleos' thought Winston Churchill a dangerous warmonger and imagined that taking on Tojo and Hitler were dangerous misadventures. My only objection to US action in WW II was that we should have let Hitler and Stalin exhaust their militaries fighting each other to the death and that we should then have stepped in and finished off the "winner" instead of allying with Stalin.
Martin Luther King was no conservative but he sometimes said things that, in retrospect, serve conservatism such as wanting his children to be judged by the content of their character and not by the color of their skin. Would the country be somehow better off if they were judged by the color of their skin? Does that make me a "neocon" for raising the question?
What has happened is that most Americans who used to be mere Republicans have been joined by those Democrats and aware others who do not want a communist dominated Demonrat Party dominating our country and necessarily joined with Republicans. If the GOP had done a better job of convincing Americans of its ideas, it might not have been necessary to welcome the heirs of Hubert Humphrey. Do you remember Hubert running as an old school Democrat for his party's POTUS nomination and being defeated and humiliated by McGovern's "rules" and communist cadres? I do. It was the end of the Democrat Party and the birth of the Demonrat Party which we know today. I thought Jean Kirkpatrick did a very nice job serving Ronald Reagan at the UN.
Actual conservatism is a far more muscular political creed than 1930s isolationism whose spokesfolks usually can be found, like ostriches, with their heads in the sand and their rumps in the air waiting to be kicked.
BMG: "I will fight and I know you will too until our cause has one day inspired the world and shown the way to a tomorrow worthy of all our yesterdays." Unfortunately Barry did not mean it and always opposed Ronaldus Maximus but those words were penned by Karl Hess for BMG before Hess himself joined with the New Left. No matter, the words are words to live by. The "cause" was not paleowhatever.