For closure, I worked on it again yesterday and got everything working correctly.
I removed the trigger assembly again and took out the washers I had shimmed the front and back with.
Looking closely at the return spring I could see that it had so much bend in it that it was being made too short to function. I removed some of the bend and got it positioned so that it returned the front trigger arm to it's lowest position every time, this was most of the reason that the set trigger wouldn't catch every time, gravity was the only thing working on it with the way the spring was set.
After that I decided to try just shimming the front of the trigger assembly with the flat head screw method. It took some playing around with the height, it turns out it needed very, very little shimming to get it right. I would say it was around half the thickness of a credit card, anything thicker than that and the set trigger wouldn't catch.
So, a bit of shim in the front and none in the back now has the hammer holding firmly and the set trigger functions every single time. Any amount of shim made the hammer hold so it wouldn't release with a lot of force pushing forward on it, but too much shim resulted in the set trigger not catching.
I gave the adjustment screw in between the triggers a drop of blue Loctite and adjusted it per manufacturers instructions plus an extra half a turn (1-1/2 turns out from dropping the hammer). The screw turned very easily and I remembered that my Renegade was that way and it was lost in short order.
Edited to add thanks to all who helped! One member even PM'd me and gave me his personal phone number so I could call if I ran into problems I couldn't figure out. I love this forum.