I use li-poly in a couple of my AEGs primarily due to space issues, they do give incredible ROF, they are mostly running around 11 volts, they out last other batteries of equal Mah and little effect from the weather.
The rate of fire is what will KILL your AEG or AEP, higher rpm tends to start gears, piston, spring etc doing strange things like.. vibration and stress warpage, leading to misalignment and then BOOM (I know this from my own experience) if you go with rate of fire, use very good parts and proper shimming.
As for your AEP, never thought of the little li=polys in the battery tray, I converted my AEP to a 8.4x1400 small battery by tether cord to my holster mag pouch, it works very well and last all day, but here again, using a li-poly @ 11 volts would likely spread the gut of your pistol all over, especially if you got an up-grade spring in it.
hope this helps