Everybody needs to identify the aircraft type they are talking about. There's quite a few different design choices the manufactures have made over the years. I'll go with my favorite, the 737NG.
737 NGs with Garrett APU can be started at FL100 t for both BLEED and ELEC
I may be wrong, but I believe all NG's have Allied-Signal (Honeywell) 131-9(B) APU's. Can be started up to FL410, with Pneu and elect. available up to FL150. On the 737NG you can run hydraulics using the EMDP's powered by the APU generator. Full APU power (90KVA) is available up to FL320 and 66KVA up to FL410.
As for powering a hydraulic EDP on bleed air. I do every time I motor or start an engine, 3000psi is no problem, although any substantial flowrate demand would drop the pressure right quick.
During a inflight shutdown, if the fire handles are pulled your hyd. supply to the EDP's is cutoff. If not, you may get some benefit from the engines windmilling. I suppose you could motor a engine on the starter to get some hydraulic press./flow. The starter duty cycle is 15 minutes on the NG.
Of course, when all else fails you have your final backup, manual reversion, yeehah.