The requirements that uber enforces on its (now) employees would pretty much have to be wiped to make it more of a contractor relationship than an employee relationship. No more banning 2-door cars or 11 year old cars, no more banning tips, no more auto-filtering out all less than perfect records, drivers would have to negotiate fares not uber, no more background checks. Basically uber does a traditional hiring process without actually hiring, whereas they'd have to move to a traditional contracting relationship. Uber forbids contracting relationships in their ToS, its specifically forbidden to hire a subcontractor. Clauses like that really set off labor boards and the IRS about "fake" contracting.
Specifically, uber would have to let the end user decide not to accept a ride in my new 2-door Yaris or my wife's 2004 Prius rather than denying for me. Also if riders consistently give me 1 star because of my HN posting habits or whatever, they'd have to let the riders decide to not accept me rather than autofiltering out all sub 4.6 or whatever grade-inflated score they use. They couldn't run a background check on me to join the service, MAYBE they could get away with running it and putting the result semi-anonymously online for the rider to make a judgement. They would have to let me set the minimum fare I'd demand, which actually sounds pretty nice for drivers rather than existing "yes/no" take it or leave it, and tips would have to be permitted.
Possibly they could spawn off a "union" or professional organization that only allows members to join that passed a background check and then only allow members to advertise themselves as part of the union. Like my roofing contractor or my unionized electrician.
There's a widely held belief, that is completely wrong, that a contractor is just an employee who is treated like dirt in exchange for more money than an employee gets; essentially a gambling relationship. The actual legal position is considerably more complicated and is not concerned with popular beliefs.