Not really.
In my case I specify models for all my m2m intermediate tables as a
matter of course. It is how I think. In my schemas, most such tables
typically carry extra data about the relationships they define -
therefore I want models. The bigint migration obviously worked for
me.
Maybe you can use manage.py to write out your m2m models so you can
adjust then migrate them.
settings.DEFAULT_AUTO_FIELD = "django.db.models.BigAutoField" should
work for new intermediate tables.
Another option is to manually adjust all your m2m PostgreSQL id
fields to bigint.
It is a lossless change and will never need to be reversed so it
might be easier to bite that bullet and move on.
YMMV