This is the second time I post my experience here. I hope it helps. I used to have a car which acted exactly like your car once. But I was far less brave than you. I turned on the emergency lights and left the car in a righ-turn lane. I had it towed to a dealer's and paid for an inspection. The dealer did not find any thing with the car and did nothing. I dared not drive the car again and sold it soon.

In addition I would like to mention I had the car fully inspected and had the transmission serviced one week before the accident.

My two cents is: Live with it or get rid of it.