After plunking around a bit, I've decided to abandon the I2C interface. Doing that with Analog I/O just takes up too much space for a FeatherWing, at least for these purposes. (If this was a full-sized Arduino Shield, that would be a different story!)
On the other hand, I'm increasingly uncertain about the MAX2268's Shutdown pin. I thought I had a handle on it, but turned out to be wrong. For now I've moved the connection from D12 to Ground; in a future update I'll either switch it back or abandon having the function altogether.
Once I've figured that part out, I'll check on the measurements for the headers and mounting holes.
On the upside, I think I've sufficiently de-spaghettified the layout that I'll no longer have to worry about that... at least for now. Of course, if I add any features, that may change.