I use a biner that is in-between my webbing and my hammock. I tie one end of the biner to the hammock using a double-looped hangman's noose (the rope will fail before the knot does) and the other end to the webbing that is wrapped around the tree. Look in my gallery and you'll see a couple of pics showing how I do it. I got the tubular webbing straps at a rock climbing store. It's absolutely indestructible stuff. I have to have something I can trust so it's worth every penny. If you want me to send you other pics of the knots I use, lemme know.
I agree with you about the biner cross-loading drama if you don't wrap the strap all the way around the tree twice first, it seems risky to me personally.
BTW - I have an HH and I kinda didn't go for the Hennessey knot, either. After looking at U-tube vids on it, I decided I didn't want to spend time memorizing the knot so I could lash up my hammock in a downpour. Many hangers use it, but it just wasn't right me so I figured out something else. Hope this info helps you.