The slack that usually goes towards the eyes, causing it to bind up, gets pushed back into the wraps with short, stiff legs. Only pushing up on the hitch, instead of pulling up on the rope to tend, also reduces the amount of binding. The Distel, Cornell, and VT are simply wraps around the rope...
I tried it a few years ago, works okay, does tend the hitch. It takes long hitch legs and has to be set each time, takes a lot of arm movement to hand tend, and it would need a short, strong connector to the carabiner.
A truncated Wrench gives an idea of the concept.
The hitches would hold for a while, but usually will start slipping before breaking. It would only be as strong as the cord holding the two rope ends, if it didn’t slip.
If it stays hung up swing it out, and back and forth, either by hand, or with a piece of rope. Try going around the back as it goes to the side to leverage it out.
Try cutting so that it moves sideways a little each time, rather than dropping straight at the tree. The top will sometimes roll out of the other tree.