The skid marks are a classic symptom of encopresis. She may have a big ol' ball of hardened poop somewhere in her lower colon that simply isn't budging, but moist, fresh poop is squeezing past. The blockage causes local numbing, so the child is often unaware of either a need to poop or the fact that some has just emerged.
I'd get another doctor's opinion. Encopresis can be serious and needs careful medical guidance. Miralax is often recommended to help keep stools moist while the child's body works its way back to normal.
An application of healing ointment plus a layer of vaseline after each cleaning may help. You might also want to look into diaper liners that can be pinned or taped into her underwear to make cleanup easier.
Good luck. This sounds like a pretty miserable problem for both of you. And unobtainable rewards will only discourage her over time. Kids generally don't need rewards when they are really ready and able to potty train.