Keith will likely jump in later today to respond to your first point about estimating models in WTP space rather than preference space...but let me give you some thoughts about using beta draws to better account for uncertainty.
A few years ago there was discussion about proper estimates of confidence bands from HB results at our conference. If my memory serves, Greg Allenby and Tom Eagle argued for using the variance in the upper-level parameters (what we call the "alpha draws") rather than leveraging the lower-level betas. If I remember my conversations with them, I think they opined that using lower-level beta draws would overstate the uncertainty at the population level. We know that doing frequentist confidence intervals on the point estimates (the typical practitioner's approach) is not statistically proper (not true to the Bayesian approach), but rather an approximation of confidence bands for the population.
Of course, you can try different approaches across a few of your data sets and see what kinds of differences in confidence bands you are getting.
And, I cannot help but point out that the method of estimating WTP from the utility coefficients will tend to overstate WTP compared to the approach that we believe is more realistic and reasonable that involves simulating changes to a feature in the test product (for which WTP is to be gauged) against relevant competition and the None. This is described at: https://www.sawtoothsoftware.com/download/techpap/monetary.pdf