One thing I didn’t see in the discussion is the possibility of a RNG artifact (not sure how that would happen, but you never know). So I tried with multiple RNGs, including the recent xorshift1024 and the PDFs generated from @seantalts look almost exactly the same regardless of RNG. Think this is good to know.
A sidenote: Some time ago I tried replacing Stan’s RNG with xorshift1024 with puzzling results - while xorshift1024 generated numbers much faster than Ecruyer when ran alone, the whole inference was slower with xorshift1024. Didn’t have time to dig in further, but it is on my “hopefully get to sometime” list.