I finally fixed my 920; I had to disassemble it and clean the proximity sensor contacts. At first, it didn't seem to help, but a bit of pressure in the top left corner and the contacts are working great. I may have to add some electrical tape to keep the pressure up on the contacts, but for now, it's fine. There was a lot of dust in there.
I used this video as guidance to disassemble the phone: http://www.ifixit.com/Guide/Disassembling+Nokia+Lumia+920/12122/1.