How can I wire this three-way circuit between two buildings with only 3 conductors?
Have you considered a remote for the house end of the garage hookup? I'm thinking a z-wave controllable light switch or something in the garage, and a remote control in the house. That way you can ignore the 12/3 romex and weird wiring (of that part of the circuit) and get on with your day.

I'm unclear whether it's allowed by code (especially with the colors you have), but with 3 wires, you've got enough for a single 30 amp circuit - ground, neutral and hot. Is that enough for the garage? That would at least be safe.