Glad to read this thread, I currently have hardware cloth inside using only staples. It's been bothering me ever since I put it up, wondering if it is secure enough. I mentioned it to DH and he brought home a bag of those screws with washers attached for securing tin roofing. Now I just need to remember where he put them, I'm going to get on it tomorrow! Better late than sorry.
For the chain link fence, what about using a straining wire bolted to the posts? You could weave the wire in and out of the hardware cloth and chain link. All you would need is a bolt longer than the diameter of your posts with an eye for the wire on one end and a nut on the other end. Once you have it all threaded through, just tighten the nut to add tension. Just a thought, not sure if it would really work, but would only take one panel to figure out if it will work.
For the chain link fence, what about using a straining wire bolted to the posts? You could weave the wire in and out of the hardware cloth and chain link. All you would need is a bolt longer than the diameter of your posts with an eye for the wire on one end and a nut on the other end. Once you have it all threaded through, just tighten the nut to add tension. Just a thought, not sure if it would really work, but would only take one panel to figure out if it will work.