So it sounds like I can get by with a driver’s license and birth certificate if I’m flying into St Maarten’s but not St Martin’s (and frankly, I’m not clear on the details yet.) I’m too far from a regional passport place to get one in time (Chicago is the closest).
It looks like you are in the hands of fate now depending on which island you are flying. You can go if it is one and will have to cancel if it is the other. I don’t think there is a way around that.
If you had slightly more time, you could use a passport expediting service. They can get you a passport in 1 - 3 business days if you pony up hundreds of dollars. You could probably do it yourself in Chicago. I got mine in 24 hours myself in Boston but weekends would hose those plans.
If you’re flying into St. Maarten/Martin, I don’t think it’s a big problem as I believe the main airport is on the Dutch side. I think everyone flies in there, save for those with private jets. Once you’re on the island, I don’t think anyone will check you for a passport if you stray across to the French side.
If you’re flying into the french side, you might have trouble.
I just want to confirm that they don’t check passports when you cross from one side of the island to the other. (The rest, I don’t know anything about.)