Bearings vs. Bushings in Gearboxes + All-Belt Gearbox?

[Colin Small]

So I've run into an issue messing around designing gearboxes. I've been trying to make an all-belt gearbox, as pulleys from SDP-SI are way smaller than gears from places like vex, and using pulleys allows you to not be restricted to having the gears tangent to each other. Since that wasn't enough of a weird idea, I thought that it'd be cool to make it two speed via a dog shifter, meaning that the pulleys would have to be machined out to fit the dog.

However, the pulleys are already the thickness of any vex hex bearing. This means that there's no room to machine out the pulley. As far as I understand, this could be solved if I first pressed a hex-broached piece of bushing material into the pulley first and then machined it down.

So my questions are:

1. Will an all-belt gearbox even work, or will I end up slipping/breaking/overstretching belts?

2. Do bushings have low enough friction so that both speed pulleys can spin on the drive shaft no matter the pulley that the dog is engaged with (the drive shaft would be idle when the dog is engaged with neither).

I hope that makes sense. I can upload pictures of the CAD and answer questions if they need clarification.