I also did a PhD on MCMC (for sampling images), and agree fully with everything you said. I'll just add that I never felt I could trust HMC at all (I hardly used it) because it was too abstract, I couldn't form much intuition about why it mightn't be mixing. On the other hand I could easily understand the deficiencies of Gibbs sampling (in my case, changing one pixel at a time) and work around them (somewhat). I came away thinking that a 'feed-forward' approximation with a fixed amount of computation (e.g. a probabilistic neural net) would have been a much superior method to MCMC.