Very interesting thread to me. I, too, always search for the elusive warm tone.
I think my ears hear different stuff than most, so this will be most likely useless, but, what the hay:
1. Re: Big Fat Snare Drum: my initial response to it was very favorable. After playing with it for a while, I decided it was really choking the tone of the snare. I think much better results come from just using a mute ring from Aquarian or Remo.
2. Re: Coating: everyone seems to go down the coating road when looking for warmth. Again, this is probably just my broken ears, but I eventually decided most coatings do Not yield warmth. To my ears, attack really changes with coating, and not in a warm way. My ears hear more warmth from clear heads, not coated.
3. Play with Vibes plugs in your ears. They nicely cut some of the highs without making you deaf, and the tone you hear - a warmer tone - is much closer to what the audience is hearing.