(a) How to make phone agents understand what's going on. It's quite ridiculous that the phone agents can't check up on Flightaware, or similar, to see the status of the plane, if the airline's own system cannot see that the plane is still parked at a holding apron. That's what I'd ask them to do.
As
fastair alluded to, both OUT and OFF times are logged automatically by ACARS, and any UA employee at a terminal can poll FLIFO to see this. The problem is not that a phone agent
can't see that you're stuck on the ground, it's getting an agent with enough intellectual autonomy to look past the
/ETA line, draw conclusions, and do what is needed.