I like your innovative thinking!
But I don't think it's going to work in that set up. Namely your legs will be a little too (read: uncomfortably) close to the cassette & rear derailleur. Actually there's a good chance they will be in your crotch, if not force you to move your legs in an awkward way which is not conducive to your goal of healing. If you look at an actual recumbent, they are designed in a way where the derailleur is nowhere near the body's moving parts.
One of my neighbors had the exact same injury as you did. He also rides - and is now back on the bike - and has a ton of training equipment that he was frustrated that he couldn't use. Guess what he bought? A cheap indoor cycling trainer. It worked.
You can always go more expensive if you want, but the point is that these things work to keep most of your fitness & form up. The higher-end versions will allow for more adjustability (read: ideal position of seat to BB).
Just look up "excerise bike" on Amazon, you'll see plenty of options.
Sell it when you're back on the bike.
|| Other projects in the works.