I think it's a valid option... but you would be best to call the office you would be applying with (if there is one near you) to see if it's worth your time. They may feel you don't fit the criteria to apply in person.
The thing is, if I contact them in advance, by definition it means I don't have an emergency! I've actually gotten an emergency passport before, it was a case where I was stopped from boarding a plane because the country I wanted to travel to required a certain number of months left on my passport's validity to enter. I got an emergency passport on the same day but I had to show my boarding pass etc to prove I was supposed to have travelled that day. And it was only valid for 6 months.
Of the two places I am going, only one has a passport office anywhere nearby (New Orleans) and that's the shorter part of the trip. Additionally that's the vacation part rather than the family piece, so that would mean writing off one day to sit in the passport office, if they will even consider me.
I think my best bet is to try and time my passport renewal application. The budget Obama signed last month funds the federal government until September. So unlikely to be a shutdown in the new few months.
I am going to look into a deed poll as well, not only to try and stretch the 3 month period but also because I'd rather send a deed poll to DVLA etc (have to change driving license and vehicle registration) than my marriage certificate. I only have one copy and it was a mission to get it from the state we got married in.