A Macintosh 512K board works fine inside a Macintosh Plus. All the connections are the same - as a matter of fact, installing a Plus board inside a 128k/512k housing with a replacement rear cover was an official upgrade option.
I replaced all the capacitors on my Macintosh 512K board for the same issue. While it helped, it didn't fix the issue.
The problem ended up being dry solder joints on the Flyback Transformer. Once it was discharged, I went over the solder connections holding it to the Analog Board with a soldering iron. Very, very easy fix. Could be worth a shot. (Just make sure to discharge the Flyback with a CRT discharge tool first!)