Whew! After several hours of work today (including two screw-ups that I had to do over), our patio is finally cat-friendly! I placed a 1-foot-high tough black plastic mesh across the black bars all the way around the bottom, and followed up with a 3-foot dark green wooden lattice. My female cat inspected it and couldn't find a way out so that's great. We are only going to let the cats on the balcony when we're out there anyway.
I'm hoping it looks decent enough that we aren't going to get flak from our strata council. The barrier I constructed is very low-key and you'd have to look hard to notice it. It's at the back of the building anyway, where nobody ever goes except the gardeners. There is no path. So I hope nobody bothers us about it. *Fingers crossed*