With help from Jim Harman, I was able to adapt the concepts in his firmware into mine. The results are vastly improved over what I was able to hack together myself.

When I first attempted this, the results were completely out of control. It turns out that the problem was that I was summing the trim value with the adjustment value. What you're supposed to do is add them to compute the DAC value, not accumulate all of the adjustment values.

In the end, this is the result:

Green is the old model, pink is the new one.

Not only that, but it's easily able to stabilize on frequency after powerup in about a half an hour (warm start). But it gets even better:

The phase is far, far more tightly controlled than the old model.

The only question left at this point is whether it's worth "back-porting" this new hardware to the TCXO variant. It's not hard to do, or anything. I just have to sleep on it as to whether it stays in the store or not.