What is a reasonable sustained current load for a typical AA Li-Po battery?
First of all, 99% of those ebay batteries greatly over estimate their battery's capacity and capabilities.  For example, I bought a pack of lithium ion batteries from ebay rated at 5000 mAh.  After receiving these batteries I tested their capacities on a well calibrated battery charger and averaged only mere 333 mAh. Some batteries had more and some had les, but no battery came even close to the 5000 maH capacity. In fact no battery even had 1/10 the capacity.

Secondly all lithium ion run at nominal voltage of 3.7 volts (except lithiun iron which have a 3.2 nominal voltage) which is much higher than you need.

Most of the lithium batteries on eBay won't handle much more than 1c. If you are looking for high amperage from a lithium ion either buy a specialist battery like RC as you mentioned or wire several in parallel. 

Don't forget that an AA lithium battery is rare, the more common size is the larger 18650. Your most economical solution is probably an 18650 battery from a reputable company like Samsung, Sony, etc., rated at around 2000-2600 mAh.  Run two or three of them in parallel into something like a buck regulator to lower the voltage from 3.7 to 2.5.  Running them in parallel would only mean that you are pushing the batteries at 1c or 1.5C which, in those batteries, will not lead to explosion.

Don't forget that all lithium battery packs should be wired to a PCB that will protect against overcharge, overdischarge, short circuit, etc., adding another level of safety to your project. The PCB are easy to find on eBay, relatively inexpensive and easy to wire up to the battery pack. 

God luck.