The joints holding the top plate to the sides, and supporting the bevel gears scare me a little. Polycarbonate is acceptably strong, but rather flexible—so much so, that it's a bad idea to assume that it will be rigid under normal driving loads. This will wreak havoc with your bevel gears, unless the structure supporting the modules is rigid enough to overcome the tendency of the modules to distort. (Then again, it's more an issue of efficiency rather than failure; those gears have large, strong teeth.) At the very least, put some bracing on the open sides, to cut down on the parallelogramming action (due to side loads). You're definitely right to put a support ring on the bottom of the gearbox.
In truth, I don't think the polycarbonate is a good choice here. Aluminum gives you several times the stiffness, and several times the strength, at only about twice the weight. Besides, if you're concerned about appearance, you can always polish or
anodize it.
Additionally, what's preventing axial motion of the gears and pulleys? It looks like you're using simple set screw shaft collars, and a pulley with a set screw hub. Especially if you allow the gearbox to flex, this arrangement will cause you no shortage of annoyance. Consider adding spacers to physically prevent axial motion. And I can't tell from this image, but if you're transmitting torque through set screws, you'll probably have suboptimal results. Please track down the resources necessary to add keys and keyways—they're
vastly more reliable.
It looks like you're relying on that belt for traction, as well as power transmission. It would be wise to test that in the pre-season, to see how much it wears when running on carpet (and whatever else you think the 2010 floor surface might be).