Thanks for the ID, @Moley, @fruitnut, and @Auburn. I've never caught one, but I suppose I need to figure out what to do if that happens.
I found one website which said (bold added by me):
Red foxes primarily feed on voles, mice, gerbils, deer mice, birds, mouse-like rodents, woodchucks, galliformes, waterfowls, ground squirrels, hamsters, leporids, raccoons, opossums, reptiles, and other invertebrates such as porcupines, and flotsam.
I found it especially interesting that I had videos of raccoon, then the fox, then raccoon again. Almost as if the raccoon took off when the fox arrived, then came back after he left. A bit surprising though, as the raccoon look at least as big as the fox.
On the negative, the page also mentions that foxes feed on "strawberries, plums, apples, and blackberries".
I only caught a cat once. I didn't need to roll the trap around to convince the cat to not come back. It must not have been a pleasant experience to spend the night trapped, as I've still seen it around occasionally, but not close to a cage.
I've done that before with a tarp. It worked well in the past (especially for groundhogs), but not this year, as the bait still ends up missing. I try to wedge the cage against something, which is what the propane tank is for. They managed to free the smaller cage from between 3 logs and tossed it about 5' (second time in the last week).