This is now resolved.
Curiously, DISabling LLDP PoE negotiation appears to be the solution. This may just be a quirk of the HP switch I'm using: YMMV as always.
So in order to get ge2 to come up, the switch config I used was this:
no lldp config 3 dot3TlvEnable poe_config
interface 3
poe-value 33
Ge2 now comes up under all circumstances, and the switch reports it's delivering 9.4W, which is still not much, but more than before. You may need to reboot the switch and AP after configuring the above.