Has anyone ever used a piece of woven fence bent into a 3/4 circle with 1 opening? A foot hold or snare at the opening and deer carcass inside for bait? Just wondering if it’s worth the work to build.

On one's own property that may be something you can try. Otherwise too much for what you want to accomplish.
If you do it i'd try making it with 2 or 3 'openings' . You would want drags on such a set up

Seems to be a popular thing up north for lynx trappers. Probably work well for bobcat down here. For coyotes i think it would be a bit limiting

It would need to be a big circle here , we can’t set within 30’ of open bait. You might want to check your regulations, a lot of states have something similar.

Coyotes shy from such efforts, unless it has been there for a long time. I have a guy here locally, that wanted to thin predators to help the fawn crop. He just knew this pen that he invented would just slay the yotes, and I tried to tell him that he was just going yo be wasting his time. After two years, he had caught one bobcat and one coon. There are much better ways to catch than spending a bunch of time building pens!

If you’re going to try something like this, in Minnesota, the bait has to be covered. I believe the rules say no traps or snares within 20 ft of exposed bait.

However, if you cover a bait with woven wire and stake it down, every meat eater and big bird in the area will work it and you should be able to make flat sets, dirtholes or snare the trails anywhere from 50 to 200 ft of it and do ok.

It's my best producing beaver set on a smaller scale when high water rushes over banks and creates large featureless flats of shallow water. Three sections of the 18" H folding garden fence corral wired to H stand holding a 330 in front of fresh poplar and beaver lure in an upturned medicine cup(reusable) wired to bait inside fence takes many spring beaver for me. Here trap has to be at least half submerged so one has to really monitor water level drop. Some grass or sticks over top of corral fence camo's them pretty well if needed. Watch the weather also as dead beaver are exposed in shallow water and sun can damage them quickly, also the now FLOCKS of scavenger Bald Eagles are ever present. This is my go to set when high water floods all the castor mounds. Though I have and like 330 floats as well a little fence and an H stand are much less cumbersome but aren't as water level adjusting. As most of my trapping is site specific - I have to be able to make a set to meet the conditions of the locations where I have permission and not just move tot the location that offers the best option where I don't. And that for me is highly variable year to year so a big bag of tricks is handy and more productive. During spring beaver dispersion I have taken beaver in isolated flooded fields between main bodies of water where they wouldn't be expected with this set as they travel to new territories. I agree also probable many better sets for wary canines, except maybe grey fox or deep winter hungry ones. Pretty hard keeping coons from going over an unwell secured cover so by then a portable cubby "box" is easier IMO.

You’ll want a big circle or the magpies and crows will knock your snares over. I think they get too full to fly and start walking around and eventually see the openings. Cover your bait to limit bird activity, it is unbelievable how fast a bunch of birds can eat 200 pounds of meat scraps.