Hey man, that's a killer observation on the Bell Brass-I've got an '84 model and yeah, the cast shell's rigidity makes it super sensitive to stand contact. I always align the throw-off right over a basket arm to dry out that 700Hz ping without losing the body; it clamps the node just right and gives a more focused crack, especially in a live room.
On stands, I've A/B'd a Puresound basket (thinner rubber hoops) vs. a basic Gibraltar- the Puresound tames the highs better while keeping the low-mid thump intact. Haven't tried RIMS on mine, but it seems worth it if you're gigging a lot to avoid that rotation variability.
For hoops, triple-flange does make it ringier overall but less position-sensitive; I stuck with die-cast for the punch. On heads, your Controlled Sound X setup sounds spot-on-I've had luck with a Coated Ambassador over a Hazy 300 with 30-strand Blasters for even more controlled decay. If you get a spectrogram of those alignments, share it; I'd love to compare notes!