Of course it is possible... I have been playing with "drum trigger construction research" maybe a few years already. I have tried many different trigger types (some comercial, some pure DIY)...unfortunatelly I am still not fully satisfied with my results. Now I feel I am getting quite close to an optimal solution, but yet I need to tweak some things a little. Those waveforms I posted were recorded with a totally undamped drum. I was just curious if it would be possible to handle this completely with Megadrum software. But indeed I was not able to change it beyond the limits you set. The only way was to ask you for it.
Right this evening I was experimenting with my Snare quite heavily damped with polyurethane foam inside and mylar head (now I prefer mylar over mesh because mesh (even double layer) is to bouncy for me). It has really nice feel; sensitivity is good (piezo loaded with 1000k Ohm ), but not equal over the area; and decay time is somewhere around 120ms and is generally nice exponential. Maybe with some cooling down and tweaking it can be usable somehow. I will need to try. I also think that a proper targeted mechanical dampening may be the key to make this work correctly.
But anyway, according to my experience you can definitely achieve more with mechanical tweaking and optimization than with electric frontends or filters etc, maybe even software tools.