The big problem here is John Lennon. By all accounts he had a great aversion to working in a group after the Beatles and with the exception of a brief window in 1974 was hostile to anything that suggested a Beatles reunion. So the question is whether or not that aversion could be overcome and if so how that might be accomplished. One way might be to have the breakup occur slightly earlier than it did historically as at least according to interviews he did not solidify his "I'll never be in a group again" mentality until September of 1969. If you break them up during the Get Back sessions for example he may be more willing to be in a group but there is no guarantee of that.
My reading of Lennon might be really off here but I think he'd be more open to an album than a group. Meaning he might if circumstances are right do an album with Harrison and Starkey but he did not want to be in the same situation he had been in prior to the split. Therefore any group effort has to be sold to him in that fashion.
This is challenging. It isn't impossible though given the three did work together independently and did record a song together. But it is difficult.
This isn't even getting into the whole Yoko Ono and George Harrison tension and Lennon's lack of respect for the "kid who tagged along"
As far as I am aware "the Ladders" was an urban legend in 1971. But Harrison did approach Lennon about being in a group together in 1973. Lennon balked at the idea. But he did cool down on the reunion idea as the Long Weekend progressed by some accounts. If you could somehow speed that process up by a year or so then he might be more open to it then. Not sure how to do that though and it gets into the whole legal problem Lennon had at the time.
I've come to view Lennon's view on his career and his future (from any given point in time) of his career as a bit schizophrenic and doublethinking. Sometimes it comes across like he did not want to be in the group anymore, and many statements flat out say as much. In other cases, it seems like he was fine enough continuing to be a Beatle. And there are the statements that he wanted to leave but didn't know what to do after leaving and was afraid to so he stayed.
I really think Lennon could have gone any number of different routes, and I increasingly become less and less assured of things as destined or likely to happen, and less and less assured that the Beatles were going to breakup. Lennon had said that it could have gone on and may have been fun, or that it could have gotten worse, but who knows. He also said he could change his mood from day to day and be quoted as saying something he didn't think later and was surprised he had said. I think the Lennon/Beatle issue and the view Lennon took of it is a lot more dynamic and less set in stone as a destined end.
Of course, this isn't even about the Beatles. It's about a group after the Beatles. I do think Lennon could have been in a group and still have been content, so long as it was something different and something he had more influence on to do the kinds of things he wanted to. I think McCartney not being the group would have gone a long way towards that. As it was, the OTL was a bit of an unofficial version of that at times, as John, George and Ringo did frequently work together (at least in the early post-Beatles period).
And I don't believe the Ladders to have been an urban legend, unless that Ringo quote is made up. There were discussions outside the Ladders name that go under its umbrella; discussions at different times about forming a group after the Beatles. That's where my mention of Harrison comes from, which did not mention the Ladders, but talked about how Harrison and Lennon had talked about a group after the Beatles, and how when Harrison talked to Lennon after the Beatles did break up, Lennon just said he was going solo and George should go solo too. It may not be named "The Ladders", but there does seem a strong argument for the prospect of a post-Beatles group made up of John Lennon, George Harrison and Ringo Starr, without Paul McCartney.
