Here we agree. I haven't experimented with battery supplies on idh tubes and honestly cannot imagine why current or voltage regulation would make any difference.
Your hearing must still be way above average nevertheless. Me, I'm vision impaired and I am sometimes told my hearing is good compared to that of others even though it doesn't seem that way to me (I suppose nature makes one compensate for deficiencies in some areas with improvement in others) but I honestly wouldn't bet a dime on me spotting the difference 😀
I'd opt for CCS for a single tube (or series chain of tubes) and a CVS with soft start (slow reference buildup) for multiple tubes in parallel.