http://drive.uber.com/oh/vehicles/ -- oHIO specific
Basically if your car fits the list, you go to a authorized uber mechanic (i think i went to an NTB, list of places is on website) They do a simple glance over and sign a paper. You fillout your personal info with Uber they run a backround check, once you are cleared you come turn in your paper the mechanic signed. They give you a log in, download the app and you are off to the races.
Your idea should work you can create your own company and use the p2p license or you can start a company with a fleet of cars and hire drivers that all use uber and funnel money to yourself and then you can pay the drivers what you arrange.
I find people needing rides on craiglist or ill hand out biz cards to uber customers and they will hit me up on the side.