Out of curiosity, and having never flown anything with wheels, much less used chocks:
The usual aviation chocks are essentially two triangular bits of rubber, joined together by a bit of string, right? Could you not tie a bit of string to them, start the engines with the door open, then use the extra bit of string to pull the chocks over to the pilot's door? So once the brakes are pressurised, the chocks can be removed without the pilot needing to leave the aircraft?
It's not ideal, but then a parking brake that stops working shortly after parking seems pretty daft to begin with, to my uneducated mind.