Answer: You buy the ticket anyway and make shit happen.
And that's what I did.
Turns out, the passport agency in Philadelphia is an absolute dream world filled with angels. Which goes against the entire purpose of bureaucracy as far as I'm concerned. A friend who'd experienced nearly the same thing answered my frantic texts and let me know there's a will-call service expressly for people like me, and like the other people I waited in line with at 6am the Thursday before my trip, heart in stomach, lump in throat. As much as it didn't feel like I would be boarding a plane bound for Paris in 72 hours, sure enough three days later I was (with passport in hand).
This trip was entirely unexpected and completely out of the blue. It was a whirlwind, with only 12 or so free hours in Paris, and just a bit more in Stockholm. But it was wonderful. The kind of trip my over-planning and nervous heart needed, an exercise in flexibility if there ever was one. My only wish was for more time, but since my hours were precious few I made the most of them: I walked. A lot. In Paris, I walked "home" from work every day, stumbling upon Notre Dame and the Louvre. The Arc de Triomphe de l'Étoile and the love lock bridge. And just the top of the Eiffel Tower beyond some trees. Yes, I went to Paris and didn't see La Tour Eiffel. I tasted all the food I could, no holds barred. After visiting Japan as a vegetarian back in college, I made the decision to always throw most food restrictions out the window while visiting another country and/or culture (while no longer a vegetarian, I avoid most dairy, gluten, grains, and refined sugars for health reasons). I ate pastries and baguettes, drank (a lot of) wine and ate copious amounts of cheeses. I was pastry-shamed by a Frenchmen in Stockholm (I had a plate of Swedish meatballs plus two pastries and a glass of wine and you know what? NO REGRETS). I tried pickled herring... liked it!
I walked miles in each city because it was the best way to see as much as possible. To take a visual tour of the architecture and the people and the landmarks. I did what I could in the time that I had, but there was so much more I wish I could have done and seen. A river tour of Stockholm, the Louvre. The freaking Eiffel Tower.
What a wild, wild thing to have happen. I learned a lot in that short amount of time, most importantly: If your passport is expired and you're leaving in just a few days, come to Philly. They'll take care of you.
Stockhomn photos soon. There are too many.