Is this a break action or underlever pistol?

A spring-powered airgun is basically a diesel engine. To increase power in spring-powered airguns, the best way isn't to make piston speeds faster, it's to increase bore size or stroke length or both. The simplest way to increase stroke is to replace the stock leather seal with a thinner one. If the chamber is the standard 25mm/1" Chinese chamber size, you can us the much thinner and higher quality Apex seal from Maccari for the TX-200. Last time I checked they were $9 and all you'd have to do is turn an dovetail adapter that would screw on the stock piston. Since you have lathe, you could do some math and see exactly how much you could shorten the piston with the new seal to maximize the piston stroke.

To soften the recoil on most Chinese spring guns, the best improvement would be to make the transfer port about .125" inches in diameter. This seems to be the optimum diameter for 25mm/1" bores. Most the Chinese transfer ports are over .130" and aren't very smoothly finished. If you don't have a copy Cardew's book, Trigger to Target, you should get a copy. It's a great read for the novice airgun tuner. After all that work on the piston and cylinder you may actually need a little more spring preload and more piston weight, Many of the UK export guns have spring piston weight or tophat to increase their power over the 12FPE energy level. I can see with good tuning, one of the .22 Chinese pistols pushing .22 RWS hobbies at 475-500 fps. That would make it a dandy 20-25 yard squirrel and bunny buster with a homemade wire stock.