I'd tap, plug and drill

After removing the block from the compression tube, check how far the threads extend into the compression chamber. Once determine how much of the breach face you can remove if you can at all. After shortening the breach plug, I would then tap the transfer port with an appropriate sized tap. Using a brass or aluminum screw to plug the hole with some very strong adhesive glue. Them drill a .118" hole center aligned with barrel from the barrel side of the breach plug. I would not drill completely through the plug from the barrel side, Just enough to see the bit come through the chamber side. I'd then flip the breach over and ream the hole to no more than .125 from the chamber side. Putting a very slight chamfer on the transfer port on the chamber size with a sharp edge on the barrel side. The sharp step will provide some turbulence but if you've ever studied gas flow in engines, the exhaust port should always be slightly smaller than exhaust pipe to minimize the anti-reversion wave or backflow. Air at 4000 psi is about 1/4 way to become a liquid instead of gas.

To take up piston slop, you'll want to add grooves for PTFE slipper rings or holes for buttons, This is how the tighten up the fit on AirArms TX-200 pistons.

A smooth firing stroke will produce more power with more consistent accuracy. This is easier to do with a lighter piston. A 420fps .22 pellet pistol that has smooth shooting cycle that's accurate will be a lot more fun than a harsh firing 500 fps .22 pistol that's not nearly as accurate.

After further pondering the photos of the piston, if after the chamber and piston seal changes, you still see just the piston when the gun is in the cocked position, I'd carefully shave some of the front of the piston until I see the back end of the seal at the edge of the chamber at the cocking slot. This may require you to remove some of the metal the inside curvature of cocking arm that's attached to the piston to make sure the piston is reaching the bottom of the chamber. A spring tophat can put weight back in your need it.