He actually had a stroke due to the stress of knowing he's basically going to be fucked as soon as he hits the States

Simplest explanation, perfectly plausible.

This is a ploy to avoid extradition that he's worked out with the locals.

Definitely possible.

The UK gov likely don't want to extradite him, but are under enough pressure from the US - who have plenty of economic, intelligence, and other diplomatic levers to pull - that they won't let him stay without putting on enough of a show to convince the US that he's no longer a threat.