Liaison worked twice for me so far, but as you say it takes at least 20 phone calls to get to that step, which is extremely frustrating, and is not a solution to the problem.
Most reps claim that it's not available, and they won't budge going to the Liaison because of that.
In fact, I had one ticket that was booked like this, but when it came to ticketing they kicked out that ticket from the queue, saying that it was "not booked with direct access". only after 30 HUCA's I got that one back on queue, and succefully booked.
But I hope you agree that this is absolutely not a solution, and this should get a lot more attention to get that fixed..