If you were my student, I'd have you opening up your upper body a bit more. This way you can start pushing his butt under him and really rounding him. It also allows him to get in front of your leg so he's going forward to the fence (it'll help get distances and start rounding over fences). You need to raise your hands off his withers. This way you can actively help left his front end, and capture that forward movement and curtail it to your needs. You can still do this with a soft contact by creating an elastic bend in your elbow.
I think you and your horse are at a good place for his age... what I mentioned is a direction you should start moving as his training is really going to start in earnest.