Brute force didn’t work so I clearly need some kind of tool that screws into the outer thread and then into the inner thread to pull the crank off. Would that be the Park Tool CCP-44, and if so is there a budget alternative?
Have the cranks got Raceface’s “normal” 24mm GXP spindle? I could well be missing something here, but I think that the end of that tool –
(like this)
will disappear inside the hole in that spindle, and won’t work unless you have something to bung in there that’s just the right size to cover the end of the spindle. (I have a small coach-bolt that happens to have a head the right size. Washers aren’t strong enough.)
If buying a new one, it might be worth getting one with a big end, which I assume is intended to overcome that problem.