A motivated coon can get its nose in or under just about anything.
Are those traps double jawed? A number 1 double jaw double coil spring trap works very well. If buying number 1 double jaw double coil spring traps today, I would buy the Sleepy Creek brand.
In the past when they were not available, I bought 4 dozen of a different brand specifically because of that design, but they have poor a poor swivel rivet, weak chain, and a pathetic ring. Each one needed quite a bit of trigger tuning. Plus, the steel is poor quality. I bought them because there were no better quality traps of that design that I wanted for a muskrat job for feedbed sets. As heavily modified they work well for incidental raccoon. Very disappointing quality and will not last decades like the traps of old.
Double loop crimped chain contributes to twisting since debris can catch in the middle of the link on the cut ends of the wire. Smooth straight link chain along with a swivel at the trap, in the middle, and the end will minimize twisting and tangles. As also suggested, keep them out of reach of brush, saplings and trees.
Where I trap the trees are valuable so anchoring to or wrapping around a tree would cause negative landowner relations!
Most of the time, excellent quality pull only dog proof traps are easier and quicker than footholds.
But sometimes, a real pocket set is desirable if a mink may be around.