The shafts keep slipping forward on him because the breeching straps are WAY too loose. There is nothing to keep the cart from sliding up through the open tugs. You may have to take 1-3 wraps of the straps around the shafts to take up some of the slack. You should have about a flat hand's width between the breeching and the horse's butt at the back.
Just because the horse is opening his mouth and fussing with the bit doesn't always mean that the problem is in his mouth. Horses express anxiety in their mouth. The problem could be the fit of the harness (pinching somewhere), a muscular or skeletal soreness issue, a mental stress/frustration issue, or the bit itself. Sometimes it takes a bit of trial and error to come up with the correct "fix". (I'm not saying he looks sore or pinched somewhere, but all of these can cause a horse to fuss.)
I wouldn't bother with the overcheck right now. It isn't necessary and will actually impede his pulling at this stage in his training. You can add it later if you need it for shows once he learns to "push" the cart. If you are getting a new harness, I would order one with sidechecks instead of the overcheck.
I would also challenge both of you to actively drive the horse. You very much look like passengers. Some of this comes from experience and time in the seat. Like Leia said, holding and using the whip is a start. You will need Fancy to go forward more with time as he gets more used to what you are asking of him. And I concur with Leia regarding your hand position. Drivers should have some bend in their elbows to act as "shock absorbers". Arms that are too straight can get tiring to hold up, and also if the horse decides to put their head down and "snatch" the reins, you could be kissing the singletree! Arms that have too much bend in the elbows have a hard time cueing the horse. And arms/hands should never rest on the legs. (I realize that your husband may not be practicing to show?
) You will also want to take up the "bight" of the reins (leftover part that is on the floor). Leaving it down is a major safety problem, as there is risk of it getting caught on something on the cart (wheels, singletree, etc.) or your feet. You can either hold it in your hand (some reins come with a finger loop to slip over the pinky) or if they are long enough, they can go under your butt on the seat (not between your legs, but to the side!
). Under your butt is probably the easiest for a novice driver.
It is good that you have a broke horse to start out with!
It would be even more beneficial if you can find someone with a "finished" horse to drive (even a big one) to "feel" how it is supposed to feel. That will help A LOT in your own driving. I remember when I was first learning to ride on my "wanna-be-a" show horse. When I got to ride a real show horse, I remember thinking, "Oh, that is how it is supposed to feel!" Then I could go back and ride my "pretend" show horse and bring him along much faster. (I was like 10 years old with a four yr. old grade QH, not a great combo admittedly, but it was what we had at the time....and I learned a lot....like how NOT to do things....
)
Myrna