the compression ratio is something that can be managed with speed though. there is a LOT of thermal mass in those pistons, so while a 1500+rpm compressor generates a lot of heat, quite a bit of that is normal friction due to metal moving past metal, compounded by adiabatic heat from compression itself. At the painfully slow speeds that the pistons run, there may well be enough thermal mass to keep it cool.
Giving the pistons a 120psi shot of air from a compressor with some filtration on it would help the pistons return back, but also lower the ratio to less than 30:1. Still well above the recommended 6-7:1 ratio used in most air compressor designs, but it essentially mimics the first stage of a normal compressor.
A lot of heat still being generated, but there are ways to keep those pistons cool and if you aren't hunting for speed out of it, which you certainly won't be considering the use of hydraulic pistons, you should be OK with air.
On the cfm calculations, pretty easy to do given the volume of the cylinder and approximate speed of the piston. Gettin the volume of that piston chamber may be a bit hard since it's not a normally quoted specification, but you could just fill one with water when you get it to validate.
Of note, this is the same principal as a Haskel gas booster, though that does require a minimum inlet pressure to cycle the piston back