cherrybim-
The story with Rabban Gamliel has no relevance here. In hilchos aveilus the issur is on something that brings extra enjoyment. In those days a shower for a normal person was for enjoyment. R’ Gamliel was saying he is an istenis so he is not simply doing it for enjoyment and therefore it is permitted for him. Showering on yom tov presents an entirely unrelated problem, that is, one may not heat up water on yom tov (at least). Istenis therefore is an irrelevant argument, just as it is not an argument to be matir plowing on shabbos.
Nonetheless, I have previously stated my rav’s position that showering on yom tov is permitted.