Another thumbs up for the local state representative. I reached out to them 3 weeks prior to date of departure. I was able to speak with a live person on the second ring (YMMV!!) and he was immediately able to assure me that this would not be a problem - just that it was actually too soon for the agency to confirm an appointment. But after a week and a half wait, they were able to secure an in-person appointment for 3 days prior to departure. On the paperwork I have, I'm told to tell the officers that I have a "customer service appointment." And FWIW, the appointment is at 7am. I suspect there's a decent block of these customer service appointments each day, outside of the bookable ones via the state.travel.gov website (9am to 3 or 4pm).