Every state has different laws, so cases must be evaluated on a state by state basis. In Florida, the Diocese is listed as the legal owner of the properties.
If the diocese is the title holder of record, then there shouldn't be a whole lot of litigation. The parish is likely to lose, and would be better off putting those resources toward rental or purchase of a new facility.
Did you see the recent postings about the case out of Pennsylvania where the court there ruled for the diocese even though the title was in the parish?