To be honest I had the exact same issues with wrists; and triceps as well for that matter getting my elbows high enough in that position. I just sat at my desk at work stretching my fingers back to my forearms, and stretching my triceps. Then for about a week or so at the end of a gym session I'd set the bar up and get into that position and let the weight stretch it out. It seemed to work for me so if you ever decide to switch to a clean grip perhaps try that.
However I see no problem with a body builder grip; I was just shit with it personally.
Contrary to what you mentioned I find the clean grip sits against my throat more, but I think that's where it sits behind my clavicles whereas before it sat more on the front of my delts as opposed to on top (could be why it kept rolling). I also had a few occasions at the start where the bar managed to sit on my carotid artery; I'd drop down into the squat, and pretty much black out, couple of seconds later I'd be standing again with no memory of the rep. Dangerous shit - but I suppose that's what the rack is there for.