New discovery:

I removed the plastic sheet from the outside of the analog board. The circuit board near the top pin of the yoke connector (green wire) is darkened on the outside of the board. I have resoldered this connection, including removing the old solder first, and it made no difference whatsoever when I turned it on again.

I still have to resolder each connection on the flyback transformer. I have visually verified each connection, but that doesn't mean much.