At the stage you're at I normally vandalise them out. Get a big flat head screwdriver and use it more like a chisel - wedge the flat under the parts I can see and break them off, trying to break the part that has the thread on it at the same time. Plastic caps usually shatter while I'm doing that and all the bits fall out.
If not I remove the bottom bracket bolt or nut now it's exposed so I have better access, then I get a knife and shave away the plastic until that remaining threaded ring falls apart. With aluminium that will be harder but is usually still doable.
One alternative that I usually try early on is to cut a groove across the ring (parallel to the BB axis) and try using the screwdriver to turn the ring using that.
So far that hasn't failed for me, so I have no idea what to do next. I'd probably use a dremel or a drill to try cutting that ring.
(I've done this quite a lot, I've been a bike mechanic. But 90% of the "stuck" ones shatter when levered open as described, leaving you picking out loose pieces.)