Thanks Alan for the tip. Update: we got the passport today, but not without some hand wringing at the last minute.
According to a memo in the Migraciones office, there has been a problem since February 2017 with the machines leased to the Peruvian Migraciones that are used to make passports. So Migraciones has issued a moratorium on 'walk up' appointments for people with no appointment. In practice this meant that although we are traveling relatively soon (in the next few weeks) and only had today to go to Migraciones in Brena due to time constraints, we were informed that we can only go 48 hours prior to leaving the country and not sooner. This we learned after a wait at 7:30am and paying the fee at the Banco de La Nacion.
Fortunately we received some instructions from the passport application technical assistance window on how to submit a written request for an expedited passport outside of the 48 hour window. Also fortunately we had brought copies of what we needed to submit for the waiver. We were told that we should not assume we would be guaranteed a waiver of the 48 hour requirement. We are thankful we brought all the documentation we could think of to demonstrate the 48 hour window would not be practical, but please know that walkup passport requests are at the mercy of the folks running the operation at Migraciones as to whether this process is a priority. Most of the people had passport appointments, but it was impossible for us to wait a few months for an appointment when we are traveling so soon.
Alan thanks again for this information; we hope the above summary is helpful for those who need to go to Migraciones @ Brena.