I know the 6BT's didn't have glow plugs, but do have an intake air heater. Not sure what the newer Cummins might have. If they have either of those items they will draw a fair amount of current before the high current demand of starting. Did you used to need to do any waiting with the key partly on, or could you just twist to start on the coldest of days?
If the batteries are toast, which sitting for that long can do to them, can you bill the custodians for the replacements and expect to receive payment?
The have it towed to where you can more easily deal with it option sounds like a winner to me. I'd expect AAA will go get it and bring it home.
I used to swerve around my hallucinations, now I drive right through them.