The warm up issue probably isn't all that much of a big deal. Most of the hot gases (about 87%) get blown out the barrel. The remaining 13% get pumped out when the gun is cycled. Hot gaseous combustion products don't have all that much heat capacity (not much heat energy per gram) because they're not very dense (remember your ideal gas laws?) and their heat transfer to the combustion chamber is through convection which isn't that fast at transfering heat.
The situation isn't like an engine cylinder which blasts away at a few dozen ignitions per second and has a high precompression factor.
I think I'll order a PEP just for MadMaxing fun. Maybe I could rejigger it into being an autococking electropneumatic Striker/CrowdSweeper shotty. Those things have a nice big carousel to stuff a combustion chamber into.
Want nearly free GBB gas?