IMO forget the mics and possible processing - and just listen to it sitting at the drums.... if it is noticeable or bothersome from right there at the kit.... then I would say, fix it, right there at the drum. Because if I can hear it being a negative from the throne - then most every other mic on the kit is picking up at well.... and I can't gate everything
But even if I'm gating the toms - I still want them all too ring out similarly... Not half one sticking out with some troublesome tone. But rather have them all ring out the same.... thus when the gate "shortens" the length of each tom's note, the ungated after ring (which will still be heard by the other mics - overheads, room mics, etc) will sound nice and balanced between the toms.
So while I get the desire to not over-dampen - but IMO there has to be priorities... and not having some ugly tone ringing out would always be my priority.... and if I can't tune it out, then I will dampen to pretty what ever degree it takes. And generally if I have to dampen too much, then it is probably a tuning issue anyway.
But Morrisman probably nailed the solution - dampen the reso a bit. Though I would never use his methods - anything internal for me is just a full stop no.... I would just take about a 3" strip of gaff tape - form a sticky side out loop with it - and place it near the rim on the reso. Why I love the gaff loop.... the loop part gives the semblance of mass for efficient muffling, while the sticky provides near infinite ability to re-position. Which for something like this I find essential - because might have to try 3-4 different position before I find the placement that centers in on that hum.
Anyway - after minimizing it the best you can - at the drum - then turn back to the mics and processing. It's just always better to use processing to enhance - not to fix problems (that shouldn't be there in the first place)
Good luck....