Zip ties for me. In my opinion its easy enough to replace the screens on these cages so I dont mind poking a few holes through it. I've had to rearrange my chams cage twice in 2 years (almost 3 years) and the left over holes are tiny enough that no bugs escape and they are not aesthetically unpleasing at the moment.
If I have to do another revamp of the cage, I'll probably replace the screen.