Welcome to CF....
This is a strange one that begs more questions than answers at this stage:
1...What is the history
of previous Owner and how was he able to prove ownership
in order to gift to NGO?
2......if vessel was abandoned, then the State has first rights of possession, so I believe this will be the crux of your problem.
3.....Where was the boat built?
As suggested above, bribes camouflaged under the name of "port fees" (without receipts) may provide you with the necessary missing entry paperwork to get you moving legally...but I suspect they may want the boat, if it has sat there a long time
FYI new boat owner must first provide a "Builder's Certificate" and proof of Ownership
to get registered....then gets customs/port clearance from country of origin.
You say you already have new registry from Austria (think of it now as your boats passport)
So what you are missing is the various stamped documents showing that the boat entered the country legally and can now depart legally
You are definitely into Bribe territory....
..... if that is the case you need to get some local advice on who to approach.
Last resort, if you are faced with a legal Catch-22 and Myanmar is being difficult, you may need to consider just escaping with boat, never to return.
Bypass neighbor Phuket and choose a small Malaysian or Indonesian port to make entry with photo
shopped stained clearance papers from somewhere distant.