As promised, I rotated the tuner chip to bring the antenna pins closer to the antenna connectors.
I also added a spot for an EEPROM, with the purpose of easily storing favorite stations. The current chip I'm using is 8K, which I figure should serve that purpose just fine, but if someone gives me a good reason to use something larger I'll at least strongly consider it.
I'd like to figure out how to do solder jumpers in Fritzing. The shunt-based jumpers are a bit bulky, and they're what I prefer for most things, but in this case I'd like to lower the board's profile wherever I can. Additionally, I currently have the EEPROM locked at I2C address 1010111, and I'd like to make it user-adjustable without filling up the rest of the empty space.
EDIT/ADDENDUM: It just occurred to me that more compact jumpers (like solder jumpers) might also make it practical to have the option of piping the output into a couple of Analog input pins. (I could do that with the shunt jumpers too, of course, but I like this option better.)