Update:
The flicker has disappeared. I packed up the MBP last week and went on a vacation. After several days, I happened to notice that it wasn't flickering anymore. I guess that the bouncing around in the car during the road trip must have re-seated the video connector, or something like that, and the video was perfect. So, when I came back home I was hoping that the return trip wouldn't undo the fix. Fortunately, it's still working fine, and I can put off the purchase of a new Mac for a little while longer.

BTW, regarding a replacement for iWeb, I frequent the XOJO software forum, and one of the members there told me that they have a web publishing product that's compatible with iWeb.
https://www.everwebapp.com/
I haven't tried it yet, and can't comment on how well it works, or how compatible it is with sites previously created with iWeb. But it's something that people may want to check out, if they're looking for an iWeb replacement.


MacBook Pro 15" (2015)
Sierra 10.12.6