Gorgeous horse! He looks great for 30!
I'm a Parelli Level 3/4 student, so I'll give you my thoughts. Swinging his hind end away can be that he is just being polite, however it is very possible that he is unconfident with you around his hind end. He could be confident with you at certain places of his body, but when his head is restricted in the cross ties (which is why Parelli doesn't suggest cross ties) he gets a little claustrophobic and the pressure of you being back there is a little too much. So play with approach and retreat. With your energy low (but not sneaky!) scratch him along his body and watch his body language. If he tenses up, raises his head, tries to turn and look at you, flicks an ear in your direction tensly, etc. then STOP. This is his cue to you that you've hit his threshold of where he is comfortable with you being. Rub that area until he relaxes then RETREAT. Then reapproach.
The reason I think it's quite possible he's a little unconfident is because if a horse wants to nip/bite or want to shove you around (dominant) they generally won't move their hind end first, they will just swing their head around. This is because dominant horses do not move their feet! In the herd, the first one to move his feet, or the one who moves his feet the most, loses the dominance game.
I have a feeling you are pretty accurate on his Horsenality assessment because draft horses can tend to be introverted, right or left brained. It's just how they are, being "cold" blooded.
One more thing, is his front end hard to move out of your way? Is his hind end easy to move away when you ask? I would absolutely start the 7 Games! You will see improvement once you do.