First off, I would suggest taking the time to focus on your position over lower fences before moving on to 3'9. You appear to be slipping your reins over each fence, so you don't LOOK like you are hitting your horse in the mouth, but the video isn't extremely clear so I can't tell exactly (maybe someone else can tell you for sure). But you are riding in an position that creates more difficulty for your horse, where even at the height of the jump- when you should be completely off of the horse's back to allow him to use himself well- you are sitting down and making his job more difficult. Even over the low fences in the beginning, you are riding the fence sitting on his back.
When you trot past the camera, your stirrups look a little long for jumping a fence of this height. I think if you shorten your stirrups at least a hole or two, it will make it easier to get off his back.
I would suggest that you practice your two-point position on the flat, which will make it easier to perfect over fences. Here is a photo I absolutely love for position (besides his hands), but you can get a good visual representation of where your position should be over fences:
I think practicing a good release will help you get a good, solid base for your position, as well. It seems like your horse is a reliable jumper, and if you feel comfortable, when you are approaching a fence, about four or five strides out, get up in your two-point position and put your hands about four inches up the horses neck from the withers, even grab some mane if you need to. This way, you won't hit your horse in the mouth, which I suspect that if you were riding with shorter reins, in a more forward position, you would be doing. Here is a photo of a two-point position:
See how his weight is deep in his heels, his leg is just slightly behind the girth, his seat is out of the saddle to relieve his horse's back, and his upper body is inclined forward? This is where you will want to be, only maybe not inclined so far forward with your upper body for walk, trot, and canter work.
I am sure others will have some great advice. Your horse is beautiful and you are very lucky to have him as a partner. Good luck!