The 20L5 (as well as the BVM series) are pretty picky with sync. In my experience, the same issue also happens with CPS1 and PC Engine on my BVM 20F1U. The Extron 203rxi might help with it's ability to reprocess sync. The annoying thing is that if you turn sync reprocessing on (I think it's called DDSP?) you lose a lot of the other functionality offered by the 203rxi (the knobs in front stop working). I haven't used mine in a long time, which is why I'm not 100% certain that it'll solve that issue.
Another way is to install a sync stripper into your SCART to BNC cable, or in between whatever you use to connect your supergun to your BNC ports. I went this route since I tend to move my setups around, and adding a 203rxi into the mix (a metal box + another PC style power cable) makes it much more cumbersome. It's also much cheaper and readily available.