Adult application, prior passport was lost but had also since expired (so it was slightly unclear to us whether a DS-64 was strictly necessary, as it was no longer valid either way). Expedite and 1-2 day shipping fees included.

• 3/14: DS-11 submitted at acceptance facility (local county courthouse)
  • Pre-filled using the online filler. Because the previous passport wasn't available for submission, it automatically filed the DS-64 online form as part of the process. FWIW, didn't ever receive an email confirming the DS-64 processing, though the system said to expect one.
• 3/21 around 11pm ET: In Progress. Locator 62 (appears to be Tucson, based on later original document returned from Western Passport Center)
  • Subscribed for updates. The email address given on the DS-11 was pre-filled, so it was apparently scanned in from the form, but we never received any emails at any stage.
• 3/22 check cleared (via ARC/direct debit conversion without an image)
• 3/29 around 9pm ET: Approved
• 3/30 morning (7am ET): Shipped (with USPS Express Mail tracking number)
• 3/30 11am AZ time: Accepted at Tucson AZ USPS origin facility
• 3/31 4:45pm: Delivered (next gen) to destination PO box in Atlanta
• 4/16: Birth certificate returned by regular mail (envelope from Western Passport Center, PO Box in Sterling VA)

A couple of notes from the process:

• At some point a day or two after shipping (maybe 3/31), the State status oddly went back to Approved from Shipped and no longer showed the tracking number. That's still what it shows to this day. If you don't have Informed Delivery to hang onto the tracking number for you, you might want to start checking for the tracking number frequently in the 24 hours after Approved, just in case.
• On 3/29 we did reach out to our senator for assistance expediting, but given they acknowledged the request on 3/30, I suspect this didn't influence the timeline and locator 62 is turning around expedited applications for everyone in about a week.
• In the response the congressional office shared with us on on 3/31, in addition to providing the tracking info, the Atlanta agency noted there were no congressional appointments available on 4/1. This tells us that there is some special pool of appointments for congressional requests, but based on this data point I would suggest not relying on it at the last minute.
• We had been fortunate to get an agency appointment by calling in exactly 13 days ahead and then canceled it upon receipt of the passport. It seems that a good approach if traveling in 3-4 weeks is to hedge your bets by submitting an expedited application ASAP, calling in for an appointment 2 weeks out, and then canceling the appointment for someone else to use (which is very easy to do by email) if you receive the expedited mailed passport in time, which based on data points here, seems not uncommon even well short of the official 5-7 week time frame.