Re: stuck in park???
That's why I have AAA Premier. 250 miles towing and less for a year than the tow you mentioned even with RV also.
Back at scanners for a Crossfire there is no one best scanner, it depends on what year you have and what you need. (and not real clear on what year/model Crossfire you have. That the engine starts and the dash works means the computers are ok. That the block stays in the dash and it won't shift means the shifter module (TCM) is not talking on the Can-Bus. With the engine started and using the rod/pencil. screwdriver method does it go into gear and shift hard ?
That you are not seeing codes bothers me. Even a basic OBD-II scanner should show comm errors given your symptoms.
Bottom line, the car should be drivable but not over about 30-35 mph.