It would work.
With two magnet rotors on opposite sides the magnets should be set up to repel, as you speculated. The field goes into the toroid at one set of poles and out again at their neighbors.
The metal rings and plywood core aren't what you want. You should have either no metal inside the torroid or a laminated metal core. (The field has to turn to run down the toroid and then again to exit at the next pole. Even with closely spaced magnets this is a rather long "air gap", so a core is a good idea to make good use of the magnets.)
The metal laminates should run edge-on to the poles and aligned with their motion. So if you use radial magnetic field at the poles (one set of magnets inside the toroid, one outside) you want your laminates to be like a "stack of washers", while if you use axial field (one set ahead of, one behind the stator along the axle) you want a wrapped spiral of strip or concentric cylinders.
Potentially you could nearly surround the toroid with magnets (C-shaped, with a narrow slot for the support and wiring) to get more out of your wire. But you couldn't do a laminate stack that avoids eddy currents for that. The best you could do is a core cast of a material filled with insulated magnetic powder, like some high-frequency toroid coil cores.
With continuous (though tapped) coils and a symmetrical core you avoid cogging, just as the air-cored designs do.
A downside is that it's hard to wind coils on a toroid. Another is that, like air-cored axial designs, you don't get to cut the air gap where the windings are by putting core material through the windings. Still it looks interesting.
