Until I can get a wife, three kids and a dog on a bike, I will occasionally have to trailer it.
I have a Canyon Dancer from my sportbike days and I've used it on the Connie. I think compressing the forks 3/4 of the way is excessive. The idea is to compress them enough that they can't work the straps loose, but not so much that the bike's suspension is no longer working. Usually a couple of inches is enough. I've never had a bike work loose. Also, when using a wheel chock all your straps should be pulling down and into the chock.