Ok, I guess I spoke too soon. After I thought I had the problem solved, and it didn't come back for a couple months, but recently it started happening again every few days. The screen would be black on wake.
So I did some more troubleshooting, and NOW I think I've found a solution that works. It hasn't happened in about a week, now. One thing I did was I uninstalled the app Tasker that I had. I'm not sure if this was really what fixed it, or if anybody else on here has Tasker, but I heard some rumors about problems that it was causing, so I got rid of it.
But, the other thing that I did, I am more hopeful about. I moved all of my apps off of the SD card, Around the same time that I got rid of Tasker, I started moving various apps to my SD card to try to speed my phone up. I noticed as I was doing so, the phone froze up and the blank screen happened twice. That gave me a clue that it might have been related to this, especially since so many people on here are flagging the SD card. I already had a bunch of apps on there, so I went back and moved everything to my device memory (which wasn't a problem since my SD card was getting full anyway). I reset the phone, and an "Android is Updating" screen came up and it looked like it was processing all of my apps. After it finished, the phone booted up normally, and it's been running fine since. If anyone wouldn't mind trying this, I'd be interested to see if it helps.
Just go into Settings > Applications > Application Manager, and scroll over to the "SD Card" tab. This list shows all apps that can be moved to the SD card as opposed to device memory, and any of them that have a check mark next to them are on the SD card. Select any such apps, and on the screen that comes up, press the "Move to Device Memory" button. After you do this for all checked apps, restart the phone. Let me know if this works. Thanks!