I guess I’m still struggling with why, for example, rate is transformed into just a single point. Shouldn’t the rate be inferred conditional on the observed sea level in every year? Calling S_t the sea level, I would expect you model something like S_t = e^{r_t}u_t, with u_t \sim \text{LogNormal}(0, \sigma_u) so that \ln S_t = r_t + \varepsilon_t is normally distributed. Then you just proceed with a normal PyMC model, plugging in the sea levels as observed, and modeling r_t = c + qT_t^2 + aT_t .
The point of my big post above was to try to elicit these functional relationships, because I think it will get you to a better model in the end. I agree you could make everything into a potential, but it’s not at all clear to me how it all hangs together (though I admit I’m being somewhat nosy and you might be perfectly happy with you model, in which case I’ll drop it)