Definitely not a sage, but some ideas immediately came to my mind while reading about your world. Been playing OOTP (off and on and very casually) for about half my life, but wait for someone with more experience to reply before doing anything I suggest!
In real life, many leagues have limits to number of foreign/international players. The CFL does this to keep the base of its player pool largely Canadian. I know from a friend who plays pro basketball in Europe that leagues do that there too. You could try a small limit at first to see what happens, and adjust from there. If only the top US players migrate to Japan though, you may want to lower Japans league prestige some, and try again. Between those two settings Id imagine you could find a sweet spot!
For rebalancing of your leagues players, the first thing coming to mind (after FA which you did), is to have an expansion. Im not a fan of expansion in my leagues personally after theyve started, as I like to keep the teams as they are once I really get going. But, the expansion function can still be useful! Set the number of players teams get to protect to whatever you want (maybe pick the number of stars the worst team has to make sure they benefit the most and you get the most parity), run your draft, then delete the expansion teams. Then, all players taken in the draft will be FAs with the leagues structure remaining the same. Run a FA draft to refill rosters.
This method is a compromise between releasing all players for a total reboot draft, because teams get to keep their stars and keep their identity. Just kinda levels off the mid tier players of every team. Backstory could be a new commish that wants to promote league parity with his takeover, and then you could also at that point artificially increase fan interest of historically worse teams and lower your fan interest some (without it being for no reason).
Anyway, just some of my thoughts! Again, back up your save file before trying my suggestions because Im no sage! I just enjoy talking OOTP and finally got around to making an account on this forum so my wife doesnt get fed up with being the only person I talk to about it haha
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