Rear mech cage stuck, how can I take it apart? This is a shimano ultegra 6700 rear mech.

The swing arm/cage is incredibly stiff where it connects to the derailleur. I can just about rotate (red arrows) it a small amount but requires a lot of effort.



I tried to loosen up using an hex key (at the blue arrow), but it seems incredibly soft and I think I may have rounded out the thread, it would not budge.

What can I do? Without any motion in that mech cage means that when I shift into the higher gears on the cassette, it doesn't take up the slack in the chain, causing it to drag along the frame and close to the ground.
Get some WD40 or PB blaster and just shoot the heck out of it. Do this a few times while manually moving it with your hands and it should start moving again. Throw some chain lube in there afterwards to keep it moving nice and clean.