On the bright side, his “hard” jump is a good thing, you don’t want him to lose it, if it means what we’ve always used the term to mean, which is a horse that snaps its front end out of the way, a round bascule and has an elaborate hind follow through with its hind end. Of course that is not easy to ride, but it is a good thing.
The most important thing you need to do is sit up and put your leg on at the base. Support your horse so it isn’t just jumping up but keeps jumping forward and across the fence. Some careful horses with good natural technique can get stuck in the air and “hang up” if you don’t keep the going forward and ride them all the way over the jumps. Low, wide oxers can help them stretch too, as well as placing poles before and after the jumps (9’ before, 10’ after).
Not sure what you mean by “driving at the bottom” but make sure you aren’t dropping him at the base. It will make everything worse. With my horse with this style, it actually helps to add leg on takeoff, even though otherwise he’s a delicate flower that doesn’t much care for leg. It keeps him going forward instead of just up. Good luck, he sounds lovely and once you learn to ride it, his jump will be an advantage!