Hey Geek, thanks for taking the time to reply.
This was my first amp build, there are plenty of things I'ld have done differently, but hey, you have to make mistakes to learn. I'm too far along to introduce a new triode or pentode into my design.
Looking at the Vibrasonic schematic you sent, the second half of the 12AX7 used in the trem circuit is a cathode-follower, so essentially just buffering the signal and driving a low output impedance. With my circuit, or how it works when I turn it on, is that the Speed dial works fine. The Intensity dial (which connects the tremolo circuit to the bias grids of the power tubes) acts as a switch. All the way up, the tremolo is on and works fine. Once I turn the dial 1/1000th of a degree, the tremolo cuts off. Turn the dial back up, and the tremolo comes back to life.
I initially thought I had a fault potentiometer for the Intensity control, so I replaced it, and had the same problems. My guess is that the design of my circuit is allowing for the tremolo output signal to be shorted to ground, likely through the Intensity potentiometer. Just for reference however, here is the original Ampeg schematic that my design largely draws from:

Again, my guess is that this is a coupling issue. Yes, an extra triode to build a buffer would be great, but even some of the 6V6 Princetons put out by Fender didn't use a buffer stage either. Hmmm.