Madball - I would suggest also having a chat to the university gliding club who have had "their own" (Quotation marks because it might - as you have seen - not be) aircraft going back many years. You may find precedent there.
Good luck.
Edited to add - just had a look in G-Info. Interestingly the EUGC aircraft were owned by a "trustee" of Edinburgh Uni Gliding Club until 2011, and are now owned by the SU. It's a similar case with the Hot Air Balloon - though this won't have flown since 2015 so not beyond the realms of possibility that they have a similar issue.
Ultimately whoever has the logbooks and registration certificate has the bargaining power...