I figured out the problem on my own, so I thought I'd post back in case anyone else has issues.
When I originally reconfigured Contact Form 7 on all my sites, I changed the "From" address to be email@example.com and then added Reply-to: [your-name] <[your-email]> as an extra header. In the MESSAGE BODY, I left in a line that said "From: [your-name] <[your-email]>" so it was easy for the recipient to see who the message was from before they started to respond. This worked perfectly and nothing else was required.
SOMETHING changed in the last few days that was causing the server to pick up that "from" line in the message body and reject the message as "sender domain not allowed." Editing that line in the message body to simply say "Completed by: [your-name] <[your-email]>" makes it work again!!
Edited to add: I realized as I was going through the maildir directories that this happened more like a few weeks ago, not a few days ago.