They have not yet received clearance forms, or have no intentions of getting them ???
As you know, you are in hold mode until the releases are secured, at a bare minimum.
If you have a contract that spells out who is responsible for what, you are in good shape.
If you don’t, there’s always a small claims court action you could pursue, if it falls within your state’s limits, to recover what you have coming up until this point in time, if your client won’t pay you without the job being completed.
But as you already know, someone has to choke down those license fees, if this is to be done legally.
You mention they are missing licenses for a good chunk, does that mean they have some, but not all ??? Or are they assuming there is no license required because some is public domain music ??? As I understand it, even if it is public domain music, the actual performance of it could be copywritten to the performers that recorded it.
Because dance is choreographed to the specific piece of music, forget substitution. You will never get something close enough to have it look right.
Good luck.