Well, it sounds like you are doing fantastic! I am training my own mares to drive, and while they are the first I have ever trained for driving, I had quite a bit of driving training myself, having driven Standardbreds both on and off the track, as well as being a driver for a small carriage business in Lake Placid NY for several years (which isn't exactly "professional driving", but I learned alot about carriages, harness, hitching, and busy, distracted driving!!). I stumbled into the world of minis when my husband relented and we compromised on minis on our small property. I thought I would miss being able to ride (I grew up riding stock horses), but I have never looked back.
My mares were a yearling and a two year old when I got them. The yearling had never been so much as touched, the two year old had been haltered and led, sort of. So I did basically what you are doing: desensitization, exposure to anything I could think of, cues to move the varying parts of their bodies, leads around their feet, bellies, and heads, whips running over them, walking over things that are scary and make noise, long walks on the road to look at cars, dogs, kids, ATV's, water, scary trees.
My two year started on a lunge line lightly, once she knew the commands and gaits and had some balance we went right to ground driving, and did that basically everywhere I mentioned above: trails, roads, gates, water, other horses etc. Then introduced cart by pulling around her, behind her, in front of her. Once she was comfortable with all that, as evidenced by her attitude and lazily cocked back foot when I asked for a stand, I hitched her. Seems overly simplified, and it is, we had many ups and downs, but no injuries or blow ups either. And she has been doing amazing as a three year old this year. But, we are taking it very slowly, and I drive her only a couple times a week, if that.
My now two year old is still in the ground driving phase, and will remain there until next year, although I did hitch her twice this year and let her pull the cart around some.
I would think that given your horse knowledge, you will do fine, keep exposing him to everything you can think of, teaching him consistent commands (I know you taught him to lay down on command already, so impressive!), and taking things slow. My two year old tolerates about 15-20 minutes of real work in one session, then the potential for things to go wrong steadily increases. If you haven't driven much, take the time you have until he matures to take some lessons on a really well trained driving horse with a good instructor. It will pay off in what you are trying to create!! Your little man is soooo cute!! Good luck!
Katie