Yes – If we did this over, I think using xarray as a datastore directly (as in arviz) would be the right answer. Then all your data is in a common, portable format, and you could even think about weird things like sampling in Stan, and doing posterior predictive sampling in PyMC3.
You make a number of good points about default places to write - there are places where libraries are “allowed” to write, but those are typically in like ~/.local/pymc_data/. I haven’t had time to look at making a PR to update this, and any such PR I would want to carefully review, thinking about how easy or hard it will be for PyMC3 to accidentally delete an important folder, or the whole hard drive!