Let’s say we took the radon example, and took annual measurements. Let’s ignore the floor part of the problem too, and just think about this model:
radon_{i,c,t} = \mu_t + \alpha_{c,t} + \epsilon_c
so that \mu_t reflects the changing mean across counties over time, and \alpha_{c,t} captures changing county offsets. We want to encode our prior assumption that the \alpha_{c,t} won’t change much yeartoyear. What is the best way to do this?
I’ve thought of a couple options, but neither is perfect.

Model \mu_t and \alpha_{c,t} as Gaussian Random Walks. We can constrain \alpha_{c,0} to be centered around zero using the
init
argument. The issue here: is modeling the walks with drift=0 enough to constrain the mean of \alpha_{c,t} from drifting over time? My intuition is that the mean of \alpha_{c,t} could drift in one direction while \mu_t drifts in the opposite direction. 
Model \alpha_{c,t} as a MvNormal. This ensures that each year will be have mean zero, but using the covariance matrix to encode our assumption of minimal yeartoyear change seems awkward.
In a related question: if this were a singleyear model with no timevariation, we would use a noncentered parameterization for \alpha_{c}. Is there a corresponding noncentered parameterization for timevarying \alpha_{c,t}?
My next step is to generate some simulated data and run some tests, but I thought I’d ask first to see how other folks have solved this problem.