So I had my second drive today, and it was a complete success!
I took a lot of what you said to heart, Greentree, thank you. He's been taught to ground tie from an early age, so it was no trouble at all to hitch him while he stood still in the arena (bridled). He never moved a muscle as I lowered the shafts over him and got the traces and everything else attached securely. I did struggle a bit with the change in hand position you suggested, but mostly because of the change in feel due to the angle, and the upright position of the whip (I've ridden dressage for years, and it was odd to have the whip essentially reversed in my hand). Though the whip DID make it MUCH easier to help him understand what I wanted, especially when turning.
We were able to successfully work though a few basic figures, and I introduced a bit of trotting, and backing up. He backs up like a total champ, but he got a bit over excited when trotting, so we basically did some quick transition work to help him understand that he has to rate his speed and stride length differently with the cart vs. the drag or under saddle. Once he realized trotting was something he COULD do (he was skeptical at first), he then wanted to do more, and a bit faster, than I would have been comfortable with. He's the type of horse who, if you praise him for something thinks, "If a little was good, more must be better!" :p
I was also once again reminded of just HOW smart he is. Since he was more comfortable with the cart this time, I actually WATCHED him start to experiment with using the harness to affect what happened with the cart. He slowed down and sped up several times, and attempted different levels of response to my rein and whip aids until he found the most balanced, comfortable way to do what I was asking. All of the aids were already in place, and I walked behind the cart for awhile before I got in, and it was neat getting to watch him think through what to do when the angle and weight of what he was pulling changed. :)