Having two rear wheels does not mean you need two shifting mechanisms. I wouldn't do it. Imagine having two transmissions for a car, you'd never get them synced.

Once upon a time, I paid my bills riding a pedicab, IE - white guy rickshaw. They are trikes. The rear wheels have a big solid (or maybe differential) axle and a single cassette/rear derailleur. I am sure Mainstreet pedicabs would sell you an axle if you asked.

Are you paraplegic? I bet that you could find a grant to build/buy a handcycle. Have you spoken to Paradox Sports out of Boulder? Mal Daly would be a great start, I don't know if you can get something but I'm sure he would be able to point you in the right direction.

Good luck. I want to see pics of a completed project.

Edit: I've personally seen Paradox build an ice axe arm for a one armed climber. I've seen them build probably 30 different feet for one footed climbers. I know they also deal with adaptive cycling. I'm not blowing smoke here. Contact them, at the very least they will refer you to a fountain of info. They may take on the project. I've never heard of them charging anyone for consultation.