Fixing a date for when things changed is kind of a sucker's game. We've got at least half a century of decisions that have contributed to the change in party ideology, which occurred gradually between the 1940s and ??? (some would say we still haven't finished). For me there are a few clear facts that help inform good PODs:
- The South was voting as a largely unified bloc of racists with a wide range of opinions on economic matters from Reconstruction until the 1960s, after which racism was only the most significant driver of regional opinion and economic policy began to narrow towards the conservative band. I think this is overlooked because the backlash to Civil Rights was so overpowering, but you do see the emergence of fairly modern "Carter-style" Dems at this time along with the more dominant hardcore racists getting fed up with the party and hogging the national focus.
- The average Republican elected official was getting more and more liberal right up until 1980, at which point a dramatic new trend line emerged. It's worth pointing out that nationally-elected bodies tend to trail popular opinion trends, so it's probably too late to change things by 1980.
- The Southern Strategy was a real thing- despite some revisionist hot takes- but it required most of the major Civil Rights legislation to be put into place and be considered a "settled issue" before the Republicans and Southern Democrats could think about a true merger. Whether it was Republican squeamishness about out-and-out racism or Southerners reading the writing on the wall and moving on (in tactics, if not in spirit) that's up to interpretation.
Then there's the major dichotomy that allowed the big tents to exist: a group of pro-labor factions vs a group of pro-business factions, both with varying opinions on everything else.
So when you get right down to it, you need something that meddles with Civil Rights. The most straightforward way to do this is to have the GOP unabashedly own Civil Rights legislation and win the loyalty of the African American community. It's a bit tricky to have African Americans come down against labor, but not impossible. And perhaps exceptions could be made- a situation where the GOP moderates a bit on labor to keep the black vote but retains enough pro-business cred not to lose their conservatives.
Now this creates a lot of tension- you have one faction that favors business but welcomes in a downtrodden minority, forcing them to have a muddled opinion on economic issues. You've got another faction that favors labor but welcomes in a bloc of racists, forcing them to have a muddled opinion on social issues. The two-party system has been tested before and has always emerged triumphant. But this could lead to another serious test. If the big tents fail here, it'll be because conservatives bolt from both factions and form a third party. Then we either see the disappearance of two-party politics in the US (the factor that makes big tents at all possible) or another kind of realignment as the three parties fight for two spaces. It seems like the ideological sorting that's happened IOTL is inevitable in that case, but maybe coalitions reemerge similar to the ones that existed in the big tent days and those days continue.
So my scenario isn't a guarantee of success for big tents. It's just the best one I can think of.