My iPhone has reclaimed its value

Fixed my iPhone.

I restored the software again using iTunes, and then immediately went into Settings and removed the gmail account. Once the gmail account was gone, I was able to toggle my MobileMe sync settings off and then back on again, and everything went back to normal.

So I can't be sure about exactly what caused the problem, but it seems like the gmail account caused some sort of corruption that prevented the iPhone from sending/receiving email, contacts, and calendars, and also prevented the editing of account settings. Going into the account settings immediately following the restore was the trick- the gmail "bug" seemingly hadn't fired yet at that point.

This is just another example of the unfortunate state of the 2.x iPhone software. It's gotten better with 2.1, but it's still flaky way beyond the standard set by 1.x, and beyond what should be tolerable on an omnipresent, mission-critical device.