OK, we are back home with a brand new passport in hands.

Here is the course of events:
- called number of times trying to get an appointment - no result, first available appointment was for Fri
- drove to Chicago Sun
- showed up at the federal building around 8:10 - there was a line to get in the building of about 50 people. The line quickly grew and was about 120 people by 8:20 when security started to let people in. Security did not care about appointments, people with kids, pregnant women - all were directed to the same line. I believe at least half the people were going to immigration office
- got through pretty quickly - about 8:45, got to 18th floor. Guard there asked if I had an appointment and travel dates - directed me to a separate room with about 10 people. There my docs were checked and I was sent to the main line. There documents were checked once again, I was given a ticket with a number. Number was called in less than 10 minutes, documents were checked yet again, I paid the fee and was told to come back from 1 to 4 pm.
- we got back around 2. It looks like there was a lot of people there at 1, by 2 there was about 20 people waiting to pick up their passports. We got ours about 2:20. If we showed up at 2:20 we would be first in line.

After all, the experience was, I would say, pleasant. Probably the best of experiences I have working with the government. Everybody was helpful. Of course they were trying to be serious about the fact that we let the passport expired, but I think only not to encourage the situation. Most people in line were in the very similar situation - forgot to renew. I only saw one person with short notice emergency travel.

Any questions - let me know, might not be quick to answer since traveling next few weeks.

Maybe relevant to this thread.
Many years ago (due to an error in issuing my pp) the laminate which covered my picture page was missing [after several intl. arrivals, it was finally detected at Newark]. Customs (they've seen this glitch before) suggested that I go to the NYC pp office; I phoned, but was informed that they do NOT actually process pps--they directed me to their office (not officially listed) on Varick St. [located in a building which also has a NYC jail]. I guess, that for most pp offices which deal with the public, that is NOT where the pp is actually "printed".
It is possible that pp "expediters", gain time by going directly to the printing office. Whether (as in my case) the public could do the same...I don't know.

This is actually shockingly common because minor passports are only good for five years. People expect that if their family got all their passports together, they'll all expire together.

Well, there were more adults there than kids. One of the issues for me was the fact that they want to see the kid and both parents. One parent might appear, but with a notarized consent from the other parent.

There are just about always more adults than kids applying.

Laminate issues on my passports was why I was often having to deal with the NYC Passport Agency back when everything was on Varick for the area. It got relocated/split for space issues IIRC and IIANM about that.

The third-party "expediters" aren't supposed to be able to access the "printers" of passports; DSS would throw a hissy fit about that -- and the "expediters" -- at least mainly -- use the same offices we the general public do.
Nice to see it worked as expected.