I hope this helps, I organized it with the most to least invasive ideas here
If you want to eliminate the problem at the source then outside of what you have already mentioned you can vent the heads. Yeah, can't really reverse it, but it is an alternative to moongels, and rings, dots. The idea is to use packing tape to protect the head from splitting, and then using a safety pin to puncture a small vent hole. More holes mean more air venting out which reduces overtones and dries out the drum a little. I would use this as a last resort… honestly. If the drum begins to give you a problem and the drum heads are ones you really like “A LOT,” and you don’t want to change heads, then I would suggest increasing the air hole size, or even adding an air hole. A lot of folks use a 3/8” vent… well if your tom is pretty large in size/volume then maybe it is bouncing the air inside way too much. Think about the bass drum and then why people move to a ported head, because a floor tom isn’t too far off from a bass drum. If you are comfortable modifying the floor tom yourself then I would get a 1/2” air vent. They are cheap, like less than $5 usually and screw on very nicely after you increase the air hole size with a drill. Think before you drill… there is an inner and outer ply… if you drill on the seam of the ply expect nothing but trouble. You can also play dress-up and skirt the drum. Crochet something nice with a little spandex band, or cut an old pillow case, and mount that puppy. It should kill some of the overtones.
Another thing... if you are using the same type of drum head on top and bottom they will tend to harmonize with each other better... increasing resonance and your problem. Next time you purchase heads try a different style of head or different ply it should help with decreasing resonance a little. I am guessing that since you have tuned up/down and it doesn’t help that you just might be using the same heads on top and bottom. I am not sure how learned you are on tuning, but for those who are not there are different theories: Tune them to the same pitch and they sing for a long time, different pitches do a phase cancellation and deaden the drum, but if you tune the heads with one being slightly higher or lower they can cause a nice pitch bend. I generally stick with keeping the resonant head very loose... trying to maintain that lowest possible pitch... and then tune the batter up a bit higher... This gives my toms depth, reduces some of the overtones, and makes them growl a bit. I have tried tuning my drums to specific pitches... it seems to mess with the drums too much, it sounds like I have them tuned way too tight. I am backing off and sticking with my tried and true method. This ends up being about 1 1/2 turns on each resonant lug and close to 2 turns for each batter head lug.
“Denial – it isn’t the drum it is everything else…”
Hope that title got you to laugh…
Remember that it might not be just the drum but the room you are working in. You may not have changed much there other than new heads... but when was the last time the drum was tuned with new heads in this spot with the furniture in this way. You can work with alternatives like dropping a thick folded blanket right under the floor tom, or adding some other sound dampening devices to the walls.
Well there it is
long winded as usual... but hopefully useful for you and anyone else
Let me know how this turns out.