You're in a catch 22. Yes, you need to push him up into the bit from behind, but if there's no contact up front, you're just going to drive him out an empty door. You have some contact, but it could stand to be tweaked a little. In some pics your hands are in your lap and your others are in front of the pommel. Ideally your hands should be in front of the pommel with your elbows resting at your sides when your horse's head is slightly in front of the vertical. When the horse is not soft at the poll and sticking his nose out, instead of lengthening your reins, keep the same length and stretch your arms out to meet him. That way when he does start to soften to the bit and tries to stretch into the contact, the only thing you have to do is bring your elbows back to resting position to take up the rein slack. Your hands should always stay in that invisible box in front of the pommel. You already look like to you have soft hands, so just be careful to keep your elbows relaxed and occassional shrug your shoulders to keep your torso relaxed while he's getting used to the more constant contact.
Once you have the contact resolve, ride a ton of transitions to help get him off his forehand. Leg yielding, circles, serpentines and shoulder-fore all help establish the inside leg to outside rein connection.