Some horses just don't respnd well to a deep seat before each jump. If your horse prefers a lighter seat and it isn't due to a training issue (meaning you can approach a jump in both a light and deep seat while maintaining control) then use a ligher seat. Some of the TB's I train prefer a lighter seat, while most of the warmbloods do best with a deep driving seat.
With that being said, you do not neccessarily drive the horse every time you sit. A deep seat can also slow and regulate your horses tempo by engaging/stiffening the abdominals/hips therefore blocking the following motion of your seat and causing your horse to slow his stride.
As a previous poster stated, make sure you stay out of his mouth while in two point. I'm guessing this is in an attempt to slow him, try to use your seat to regulate his tempo _and this can only be acheived by using a deeper seat). If you'd rather not use a deep seat the whole time, than only use it when going around a turn of when you are preparing to stop or collect.
I think I may have a suggestion as to why your hrose is boting. You are very loose over jumps, in one pic you are getting left behind and sitting before he finishes his jump. If you reoutinely do this, your hrose will anticipate this and rush the jumps to get it over with.
You are also throwing yourself forward over each jump, very ahead of the horses motin. A hot horse will feel this sudden, thrusting motion and react accordingly. A steady seat to, over, and after the jump will encourage steadiness in your horse's stride before and after the jump.
Make sure your horses faults are not due to errors in your riding position.
I would shorten your stirrups a hole or two, right now your are reaching for your stirrups and thus loosing your lower leg to the rear. It is rotating back into your horses side and this could also be another huge factor in your horse rushing.