The adjuster looks like steel to me? Is it magnetic? I'd look to be using penetrating fluid/WD40/GT85 as you have been doing. I'd look to file a flat on the head for a good grip (looks like you might have done that?) and use good mole grips or locking adjustable spanner to try and remove/prevent slipping.
I think you've tried all this though?
Next step would be to drill it out from the inside using a pistol/cordless drill from the bottom of the adjuster.
I'd slowly increase the drill bit size. I'm lucky have a nice Dormer set that go up up in 0.1mm increments, but a set which go up by 0.5mm should suffice. If the adjuster is M5 the tapping drill is 4.2mm DIA which means if the hole is central (concentric) to the thread then by the time you get to around 4mm and you twist the top with your wrench it'll probably start to collapse and twist out. Maximum size I'd probably drill out is about 3.5mm and try and unscrew, if still stuck then I'd jump up to a 4mm. You can get cheap carbon steel taps if you need to clean out the thread on the frame.
ALSO, this is assuming it's an M5 adjuster! Measure the thread, this should be around 5mm (but probably less from the threads being rolled/formed.