I believe you're right on the ground identification because it ohms out with the "-" on the battery terminal. However, if I connect the grounds (computer and chrono), my transmit path to the chrono stops working. Without the grounds connected, my software correctly controls the chrono with RS232 levels. However, I can not get any information from the chrono. When the grounds are connected, it seems to bias the signal up so that I do not get the full -12V swing ... more like -5V and software stops working.
Surely someone has successfully done this - we just need to find them