Another update. I was contacted by someone at Topaz. They got me to send a bunch of info about my computer and sample files. They had me try a few things on my computer, and finally let me try downloading the latest version of Photo AI. Still the same issue. I notified them them it hadn't worked, and I haven't heard anything from them in a week and a half. I'm not overly impressed with Topaz's customer service.
I have gone back to using the standalone products exclusively. Unfortunately, there are no updates or improvements being made to them, and haven't been for a while. I would have appreciated them at least telling me, "Sorry, there is nothing we can do at this time." and perhaps let me know what the issue is. Obviously, not everyone has this issue, and it likely has something to do with either the hardware on my computers, or some software, or settings that are interfering with the program.