Ive looked at this a few times over.
I dont have correct answers just ideas.
The two flanges that are screwed together are stuck or the piece they connect to directly?
Any stripped socket or screw can be turned into a flat head screw with a dremel first. if that fails they can be drilled out. [last resort]
How good are you at soldering?
In the automotive world many similar issues
If I were to takle this i would clean the hell out of the piece and solder a drill bit or impact bit on and then connect it with the impact driver where u soldered on whatever attachment you used.
I think with slow and concise use [wrap engine or screw down so its stable] as long as your solder job is stronger than the "stuck" part the vibrations may pop it off
this is how you get a spark plug thats stuck out. Solder and torque. Sometimes they need to clean and resolder a few times before its successful. a Penetrant oil will help [after soldering do not use around heat!]
After just take the top removed flange heat the solder off and reclaim your bit and clean up the piece.
You must use an impact driver a drill wont work. Or if u have any other high vibrations device. Maybe a torque wrench but prolly overkill. [or try a Beach Boys album I hear they have Good Vibrations]
Good Luck
Offering only ideas and not solutions maybe you will run with!
Jason