It sounds like that orange web flexible plastic that is called "snow fencing" or "construction barrier fencing" might serve as well if the fence posts would keep it taut. It's made with several different sizes of openings, and many are big enough to admit small critters, toads and snakes --- I love nonpoisonous snakes --- but would keep out adult cats. The only thing to worry about would be something small falling through the holes and not being able to figure out how to get out. I'm thinking of toads and kittens, primarily. Snakes and chipmunks should have no problem with the larger mesh sizes.
I Googled "snow fence" and only looked at one seller, but I saw enough to believe it would work. They even sell something called a "slotted T-post" which might do the job of the original chain link posts IF they are heavy enough to hold the mesh taut, and eliminate the need to tie the webbing to the posts. (I keep envisioning kitty trampolines, for some reason!)
The fencing comes with several size openings, in different widths (4ft and 6 ft) and lengths, and even in inoffensive colors, like black and green. So it would work with a bed four feet wide, but not three. Anyway, it's something to think about.
(I don't remember if I'm allowed to post a link, so if I'm NOT, please remove it.)
http://www.discountfence.com/s...