Quick question that hasn't been asked; are you a good/experienced drum tuner? (And don't feel bad if you're not, most guys aren't!) My next question is: How high/tight is the drum tuned?
It 'sounds like' the drum is just choked.
You mentioned that it rattles the hell out of the snares in sympathetic vibration. The snare drum is usually tuned high; reso to an A note and batter to a C or higher. If you're getting a lot of sympathetic snare noise, you need to take the tom into a different tuning range, likely -down-.
Flip the drum upside down on a rug or a towel, something to damp the batter head. As you re-tune the reso head down, do it in very small increments, 1/8th of a turn on the key at a time. Go around the drum loosening the tension slowly and tapping on it until you hear it open up. There's no mistaking the sound. All of a sudden you'll hit a sweet spot in the tuning range and the sound of the drum just opens up.
If you like what you're hearing... make sure you hear the same pitch coming from the head when you strike it about 1" out in front of each tension rod. Get the head in tune with itself. That done, (you hear the same pitch in front of each t-rod,) flip the drum over and reproduce the exact same pitch on the batter head so that both heads sing the same note when struck. Takes a little time and practice, but I'd try re-tuning the drum before buying new heads, or drilling vent holes, or stripping it down for mechanical inspection. That's like checking for cancer because you have a runny nose.
Could be as simple as tuning the darn thing right. Every drum has a spot in its tuning range where it opens up and resonates. If you can't find it anywhere in the drums tuning range, then maybe the problem lies elsewhere. For now, try re-tuning it. Experiment.
Also, if you take the high tom down, you'll have to re-tune the other toms. At least they'll all sing for you when you hit them. The combination of symptoms you described, (if I was paying attention and I heard you right,) is; a choked tom that creates sympathetic vibrations with the snare. That is a 'tell' that it's likely a tuning problem.
John
