I have a tank divider like that between my Male Betta's, and of course they discovered each other. What I ended up doing was going and getting some of the "wallpaper" used to decorate the backs of tanks, and putting that on the divider. It worked like a charm, and I don't have two puffed up Betta's anymore....
I also didn't want to chance putting paint in my tank.
a new tank also sounds like a fantastic idea, though!