For now, at least, this sounds like a problem where human involvement is really useful.
Cranky Concierge, as someone mentioned below, is one great option.
Another is paying the ~$50 for lounge access for the day, to talk to the reservations agent at the desk inside the lounge. They're usually much more experienced, much more likely to spend the time to do creative routings, and haven't just had to deal with possibly several hundred angry passengers. In one case with United, I stepped out of line to speak to the gate agent after my flight was delayed several hours and paid to go in the lounge. I wound up getting the last confirmed seat on the next flight, whereas the person just in front of me in line had to go on the standby list (which she didn't clear). That $50 was _well_ worth it.