Well, I think I've proved it's Avast!...

I tried turning off the entire File Shield System and typed for nearly an hour without problems. I turned it back on, saved without trouble, and then set the document aside to watch Get Smart. When I came back to the document, it started right in giving me trouble with that idiotic file permissions garbage. Once it starts, it doesn't stop, not even if I close Word and open it again. But I turned File Shield off again and didn't have any more trouble.

I've noticed it seems most likely to cause trouble if I've had the document up for a while, and especially if I've left it for a while and come back to it. I suppose it's a security measure in case it isn't the same person coming back to it, but since here it always is the same person, it doesn't help me and is just a detriment. I wish I could turn that feature off without disrupting the whole program.

Ugggh, uninstalling and reinstalling and fooling around in the Avast! Safe Mode and all the other stuff they said to do is not going to be fun....