I am sure you are not going to get a counter agent to tag it to MDW.

If your bag gets gate checked it will be treated as though you checked it at the gate. It will end up on the baggage claim belt at IND not MDW. That is probably what will happen if they gate check a car seat as well since you wouldn't have any use for the item during a layover unlike a wheelchair or stroller.

My recomendation would be to either deal with car seat the car rental company gives you and carry on and make sure you are at the gate to board on time since you will require bin space and can't afford to have your bag gate checked.