I think its important you get that speed sensor in the rear out. Are you able to possibly get something around it (adjustable wrench) and turn the sensor to free it up. Try spraying some PB blaster on it and letting it soak in. They aren't too tight of a fit, so hopefully you have break her loose and then pull it out.

Also, it could be that the sensors are clean, but one of them has gone bad. Not sure how to check if the sensor is bad though.

As Wood_e said, it could be internal with a tooth knocked off. Don't know how you would check that either though without pulling it apart.

I say def get a second opinion. This should be a much cheaper fix than thousands of dollars. The problem is just finding out exactly what is wrong without spending a mint trying to find it.