You would not recommend an equitable distribution hearing as I was told may be the next step?

I just don't expect it to help.

Hypothetically, if an equitable distribution hearing was to occur, what is the process?

Attorney files motion and notices all relevant parties. All parties' counsel show up and argue how much they are owed. Judge sometimes orders a pro rata payment schedule to the relevant parties; but that is when they are all unsecured. Public hospitals are secured by liens by law; so they don't have to knuckle under to the judge's ideas.