It is hard to tell because most of the time the video is from the side, but it looks like he might be tilting his head to the side. This could be why you are feeling the resistance to the left.
Do not worry about being slightly behind the vertical right now, it is only because he is fighting you and trying to avoid the contact.
I think it will get better as his back & neck muscles get stronger. I don't think a stronger bit is the answer, but rather do more transistions using your seat more than your hands. You must keep this horse busy to stop him from fighting you. Try more lateral movements, my favorite is a spiral in & out and 10 meter half-circles for change of direction. Build up to shoulder-in as soon as possible.
The lateral movements will help him to hold his frame. You do not want to get into a habit of fighting him for his head every ride! Ask nice then demand! It is not your job to hold up his head:)
He is a bit too much on the forehand, which is why he is leaning on you. Try some walk to canter work to help him use his back end more.
You two make a lovely pair & he has a lot of potential once you get him to work with you instead of against you!
I did not see the first video, but the second shows you are on the right tract and you look to be a very capable rider!