Agreed - I have welded wire on the top of my runs. If the Premiere electric netting is too expensive, you can run a few strands of electric fence wire around your coop and run, starting a couple of inches off the ground, and then one every 6 or so inches up. I have 2x4" welded wire around my run, with 24" high hardware cloth around the bottom to keep chicks in and other animals from reaching in and snagging them from the outside.Sorry to hear about your lose...
Yes, foxes can climb very well, grey foxes hang out in trees regularly, so can raccoons and possums, bobcats and several other predators... While coyotes and bobcats can clear jump a 6 foot fence without the need to climb... The short of it is that a 6 foot fence it ineffective on it's own, you need a wire roof or solid roof to prevent climbers and jumpers from gaining entry...
And this goes for electric fences as well, as I said a coyote can clear jump a 6 foot fence, so even if electrified they can simply jump right over it, while smaller digging predators many times can dig under or simply go through the fence getting around the electrification, thus the reason 1/2" hardware cloth, buried and skirted is recommend....
How our run is constructed, and how we hold the wire up so it doesn't collapse under the weight of snow.