Things have not progressed and it's getting frustrating. At this point, both A/C companies that have come out to assess our problem have independently said the A/C needs replacing and that the furnace needs to be replaced as well - it's fine but a different system would work better with the new A/C. They also both noted that the system was installed upside-down. :/ So we contacted the home warranty company to find out what they could do for us, because though they don't cover our A/C, they do cover the furnace. The agent said that they would cover the furnace, but they need the formal assessment from the selected company to be able to create the work order, and that they'd contact them to get it.
That was over a week ago.
We've gone back and forth between the contractors and the home warranty company, and it's at the point where the former is saying the latter hasn't contacted them and the latter is saying that they did contact them and received the report but it's incomplete so they can't move forward. I'm not sure which side to believe. The contractor's office guy didn't remember when we called him on Thursday that we had talked to him on Tuesday about this. On the other hand, the home warranty agent assured us that they knew the report was incomplete and that they would contact the company right away to get the full report - implying that they weren't doing a damn thing about it until we called.
So, we're still stuck in the same boat. It's been five weeks since the A/C broke, and four weeks since we moved in with our friend, and we still don't even have a clue as to when anyone might start working on it. On the bright side, we're halfway through August, so in a couple of weeks, we can probably move back home just because the weather will cool off. Sigh.