Have you tried a dog shock collar? Set it on medium and when he touches something he's not supposed to, shock him. If that dosen't work, you can just keep him in his cage.
Just kidding....
A small baby gate would work but would be a pain. I'd put a small latch that you can reach from the outside to unlatch. In an old apartment I had, I used a small latch for privacy that was made for a window latch. You had to turnit to unlatch it. It worked well, and was very small. Some people put plexiglass over the lower screen as well, so their kids don't push through the screen accidently.