It sounds to me like you don't have the arbor screwed all the way into the receiver.
Also, I'm somewhat confused by your saying the pins on the base are flush with the barrel holes.
The two pins should be completely inside the two holes with the barrel tight against the frame.
Maybe that's what your saying but I somehow see in my minds eye the barrel bottomed out on the arbor, the wedge installed and the lower part of the barrel just touching the tops of the two pins.
That would explain why the cylinder has 1/8" of fore/aft play.
If my minds eye is seeing things correctly, you need to screw the arbor into the frame at least another two turns.
If you do, I suspect the arbor will be as tight as a mosquito butt stretched over a rainbarrel.
If it isn't, buy a small vile of the RED Lock-Tite thread locking compound.
Remove the arbor and apply a few drops onto the threads and then screw it back in place.
This Lock-Tite compound stays fluid until the threads are tightened. That activates it and it will set up in a few minutes.
Be sure things are put together like they should be. The RED compound is for permanent installations and once hardened, temperatures over 350 degrees F are needed to break it loose.