Sorry to hear about the problems with the silencing kit.
I just installed the kit on my Dad's Timney Trigger and it would not fire.
I installed the material to the hammer similar to the image below.
When it did not fire, my first assumption was that the front end of the hammer (which did not have any silencing material on it) was not making contact with the little arrow release on the bottom of the cocking sled.
I had installed a small square of silencing material to the arrow release on the bottom of the cocking sled per the instructions similar to the image below.
I think the idea behind that small square of silencing material on the arrow release is to shim out the arrow release so it makes contact with the bare hammer in addition to quieting the hammer striking the release.
In my case, it didn't seem to be making contact so I re-did the silencing material on the hammer and ran it the full length of the hammer like the image below.
Now it fires.
So in conclusion, I would recommend that the silencing material be applied to the entire length of the hammer for both Timney Triggers and the PSE factory trigger.
Those are the only two trigger systems I have experience adding the silencing kit to.
Note that the final image above is of a PSE factory trigger's hammer. You can see where a couple small pieces of the adhesive material were added below one end of the silencing material to shim it out as per the instructions that come with the kit. The Timney Trigger's hammer requires the same shimming.