HyDoR

Goodyear makes a belt called the Eagle PD. It's actually quite interesting, as Goodyear claims its double-helix design decreases noise and increases traction. This is generally true for gears, so this sounds reasonable for belts, too. It might be a little expensive, but I think for us it's worth it. (Don't pay attention to the list prices. McMaster-Carr has them for about half of what Goodyear quotes, and you might be able to do even better, as in my experience McMaster-Carr is always a little high on its prices. I can't link to it directly, but it's under the title "Tire Track" Endless Rubber Timing Belts and Pulleys on page 981.)

I don't know about real-world efficiency, but they claim that it can reach 98%, which is about the best that anyone claims for gears or chains, too. I think as soon as I settle on a layout (either a triangular layout with a separate sprocket for each of the motor, engine, and wheel shafts, or a standard belt layout with an IVT planetary gear set combining the motor and engine.

No mention of whether the belt performs equally well in both directions. Due to its design, it seems logical to me that it would slip more easily in the direction of the herringbone, but human logic doesn't dictate physical reality. I can't actually talk to a belt engineer right now because the Goodyear plants are on strike. (Who would have thought here in Europe I'd be bothered by an American strike? Go figure.)