Charging for use of the road is the only way to balance supply and demand for road. More at peak times and a discount off-peak. Fixed price subscriptions for your commute.
But I see no reason to treat Uber cars differently, except that having a driver does not qualify to one to use the carpool lane (which I would eliminate anyway)!
I'd also allow subscribers and those who buy ahead to sell their prepaid trip when the price surges. Wait an hour and make $5 when there's an accident.