N. Six
Based on your description, you don't have a problem with the thickness or thinness of your Caps. You have much more involved problems.
First step is to check and correct the Barrel to Arbor fit to insure you have consistent Barrel to cylinder gap. Optimum B/C gap is .005,
Insure, when the Cylinder is pressed against the barrel breach, the Hammer actually touches the bare nipple. Those that council the hammer should never touch the nipple are behest of HORNSWAGGLE.
Then look inside. You need to clean up the innards, eliminating burrs and actually fitting parts to eliminate parasitic drag. Pay particular attention to the Hammer Channel and polish the sides of the Hammer.
Make sure your thumb isn't riding the hammer down??
Don't forget to polish the hammer face, deburr the Safety Pin slot and lightly round over the bottom of the slot and hammer.
After doing all of this, if you want 100% reliability, you will need to add some form of mechanical block to keep caps out of the hammer channel and action.
Stay Safe Out There
PS: Pay attention to the Parts "Other Mike" mentioned.