Although I wouldn't call them matrons, the lounge attendants have saved us more than once! Once on a misconnect from AA to BA in LHR the gate agents kept ping-ponging us back and forth between the 2 airlines, each saying the other would issue a BP. We retreated to the BA lounge, where it was easily resolved (too bad we ended up aith a 7-hour layover). Most recently, our DL flight from MCI-JFK was diverted to CVG and there were 2 agents to re-book everyone. One agent was immediately occupied by a couple with a connection in ZRH to somewhere in Africa. Pulled out the PriorityPass and found the nearest DL club (unfortunately, not part of PP anymore). The lady there was wonderful. They'd trashed the aisle seat assignment from JFK-EDI that I'd begged and peaded for earlier (we have no DL status) but she got us into aisle seats.

I did end up at a disadvantage bypassing a line in DTW when they wanted everyone who had no prayer of getting out that night to step aside and wait for them to rebook the others. I probably missed getting a breakfast and dinner voucher, but got my rebooking info on the phone as I hiked to the DTW Westin and got settled in my room earlier. Best I could do under difficult circumstances.

Short answer: the airline's lounge if it's an option, otherwise hedge my bets by waiting in line and calling on the phone.