If you can't get it to sound the way you WANT it to sound, accept what you get or get rid of the offending drum or drum set.
Like Cam said, I get this sentiment as well. In the broadest sense, sure, if you can't get the drum to sound the way you want it, get another drum. But context plays an important role here, namely that the OP's tom doesn't sound the way he wants it to sound when mounted on a snare stand. Hence, the ask for ideas, which many have generously offered.
I agree with the OP...while I like the look of the high tom mounted on a snare stand, I didn't like the way it sounded. It's a great sounding tom otherwise, and its resonance was nearly non-existent in a snare basket. It sounded dead. Had it set up this way for a few days, then I reverted back to the original bass drum-mounted arm, which of course limits placement (and actually affects the bass drum sound, though not significantly).
It doesn't matter whether a recording engineer or audience at a gig noticed a difference, it was noticeable to the OP. And considering that I've experienced the drastic tonal difference between mounting my tom vs. sitting it in a snare basket, I don't consider wanting to let the drum breathe more as "obsessing." This is not the same thing as putting felt in lugs or using plastic washers...or hanging the drum from fishing line.