You need a 'midi kiti-kat' or something along those lines, basically it uses microphones or transducers to 'trigger' a 'gate' which in turn creates a midi note. The above mentioned unit I think could do 8 or 10 channels, so the full kit. One of the alesis drum modules also has this function and I think akia also made one. I have used all three in studios and had a drummer who used the alesis live all with great results, however if its just for studio use logic audio has a audio to score function which generates midi notes from audio, very clever!

Your namesake 'ddrum' and others make triggers, but you can get it done with cheap $2 piezo transducers.
Hopefully you're augmenting good sounding drums with good mics. Ideally if your front-of-house mixer has Direct Outs on the channels you can use those sends to feed a drum brain. That puts control of those sounds in the hands of your soundman.

I always felt there would be too much latency converting audio to MIDI and back to audio for live use. I could be wrong about that, but since there are drum brains that have trigger inputs - that's what we used (15-20 years ago). We had the acoustic kit sounding good and were able to mix in some electronic samples from a Korg DRM-1 to enhance the acoustic kit or change the flavor. We just did kick and snare using cheap piezos from Radio Shack for triggers.

ddrum used to make a concert quality drum-trigger brain. I've recorded with the Alesis before. We used a Korg live. The ultimate concert drum trigger rig back in those days was the Wendel Jr.

The drummer broke a top head on his snare one night mid-song. He missed 2 or 3 beats before the soundman dialed up the snare and we finished the song with a 8" rip in the head. It took 15 seconds to throw a little duct tape and cardboard on the head between songs and we finished the set with the triggered snare. The audience probably never noticed the broken head.