I pulled all the pieces back together after 24 hours of drying time, and my patience was rewarded with a working cell phone. You might notice that the phone didn't make it out all together unscathed, as there are some strange bright spots on the screen now. They aren't really noticeable except with a solid color background, so I consider myself somewhat lucky.
All the buttons are working, no data was lost, and the speakers and microphone work just fine. The camera is working, and I can even complete calls with the thing! Steve Jobs won't see any (more) of my money for at least a little while longer.