Tuning Kalibrgun Cricket Standard Depinger

The "ping" on my Cricket II is pretty clearly the action (hammer and valve) and not a shockwave in the air cylinder which "depingers" address. It reminds me of a "twang" some early Vulcans had. For the Vulcans a short rubber sleeve on the hammer spring was the fix. There is no room in the Cricket II for anything on the spring OD.

I've had an original Cricket for a few years and it has been my standard for quiet. The action noise of the Cricket II is my only disappointment and I've been looking for a remedy. Was hoping CF or one of the other gurus would come up with a fix.