I'm honestly just curious how others would do this. I've never had this issue, but the people I play with are pretty easy going for the most part. If I was hosting I could probably just do it whatever way I felt was most fair and most likely no one would complain.I’m rusty on this but I think it’s usually a first in first out type thing in a card room if no one volunteers to move from the must move table. In a home game I might grab a player based on position of the empty seat in the main game assuming everyone sat down at the same time.
I think you might be overthinking this though. If it’s a friendly-ish game, just merge the tables. Who cares, path of least resistance/effort. If somebody has an issue you can address it then.
If your home game is more serious, if the rotation or stakes are different and the table breaks, well it breaks and those players can buy in up to the max in the existing game.
EDIT: As stated above, some could see it as going south if new players have to buy-in again.