[asid61]

Lightweight CVTs for FRC are at the moment nonexistent, and it will likely stay that way due to their nature. All of them are friction-based or hydraulics-based, which means it's either illegal (by 2016 rules) or difficult to engineer. I tried my hand at making CVTs a couple years ago and found that it was extraordinarily difficult.
If you want something very close to what you envision, a 2-stage ball shifter may be your best option. You can design a ball shifter shaft capable of switching between 4 or 10 ratios very easily, as long as you can find a cylinder or linear actuator capable of shifting between them.