I haven’t looked at all the context of the problem, but I have been in a similar situation with pymc2. I wanted to apply a prior-distribution to a deterministic variable.
Fortunately, I had symmetries on my side. I made up a dummy data-value with the central value of my prior distribution. Then I told pymc2 that the dummy-data varied according to the deterministic variable. And in the wash, I was able to show that this was the same as applying a prior I wanted to use. That may or may not work for you.