I wouldn't lengthen your reins at all, you're not hanging onto his mouth much at all, he just looks to be the type that will suck back to evade the contact and just needs to be driven up more into the bridle ;)
Biggest thing that stands out to me about your position is that you are collapsing to the left. Your right shoulder is being carried higher than your left, and as a result I would say that you are losing your balance slightly to the outside. This will make it difficult for you to ride a horse dead straight, there will also be a little bit of head tilt, crossing of the hind legs or swinging out of the quarters of forehand. Not one person has got dead even shoulders, but you can improve on it. Best thing you can do is get mirrors in the arena and ride towards them to look at where your body is leaning. Imagine you have a pair of braces on holding up your pants. When you lean to the left, the brace on the right pulls tight and the one of the left goes slack. Try to even your body up so that the braces pull at even lengths.
You appear to be gripping with your knee slightly, with the toe turned a little out. Keep your toes pointing forwards, matching them with your direction of travel ;) As for the gripping knees, this also brings the heel up and the lower leg off, losing the effect of your aids and your balance will go over the front of the horse, putting him on the forehand. Even so much as a glance downward can put your horse on the forehand, so leaning forward or having your weight forward is going to have a marked impact. Rather than shoving your heels down so that you feel tense in your thigh and lower leg, focus more on sitting back onto your seat bones, and letting your weight flow run down the back of your thigh, the back of your calf and into your heel.
I'd also like to see your foot a little further back in your stirrup. Yes we are told the ball of our foot, but to be able to use your weight aids and leg aids most effectively, with the best balance possible, the stirrup must rest across the 5th metatarsal joint (your little toe) - so the 'knuckle' where your little toe joins the ball of your foot. Make sure the stirrup does not sit at an angle on the foot or again, you will lose some effectiveness of the aids.