I've now tested 4 PSU's in total, original, new one, PC Engine 9V 1.5a, and a Megadrive one which is 9V 3a.
I've noticed that if I load up a game, say Real Bout Special or RB2 it'll be fine, but if I use a hotkey swap, and then go back to Real Bout, the lines appear, and if I power off and on...