For future reference. I don’t think the problem I had was with the horizontal sync but was a ribbon cable issue similar to the one described in this article https://www.ifixit.com/News/12903/flexgate. Not that it matters much because the solution is the same replace the whole screen.
I decided to try my luck and took it to the Apple store. To my surprise the lady there immediately identified the issue as a display cable issue that was replaceable under warranty (in Australia at least) and for good measure they would replace the keyboard AND BATTERY. The only condition was that the moisture detectors inside hadn’t gone off. If they had it would have been an AU$1500 fix.
So now here I am with a refurbished laptop, new screen, new keyboard and battery for absolutely nothing.