Inspired by Collingwood's knot -- which I would just call a parallel constrictor -- has anyone considered doing a parallel clove hitch?
Meaning, after tying the clove hitch, go again in parallel to the knot. You need to go in an exact parallel, as in the double figure eight in rock climbing. Same as the clove, you will get a symmetric knot. It will look a bit like you've tied a clove hitch with two parallel ropes
I'm pretty sure it's more secure than regular clove, but of course takes an extra couple of strokes to tie
Now, if you take it off the beam, you'll find that it's just a twisted straight knot with an extra loop laid on top of it. So, similar to Collingwood's "boa knot", you can tie it by making a straight knot, then laying a loop along it, twist the whole thing and thread the beam through the two formed loops. This way is a not much more complicated than the boa knot, but looks completely symmetric