my tuppence, ONLY on the basis of working on something very similar with my pro so please regard as my 'suggestion'...
Having paused the first video when the club is parallel to the ground, it definitely looks a little too much on the inside which then naturally takes you into a lower plane on the backswing, from which you have lower, more 'round the body' swing.
Another aspect of this appears to be that there is a little 'steering' of the arms and a little drop in the body through impact to compensate and generate extra speed/power.
If you want to get the hands higher in the finish, this needs to come from the plane developed at the beginning of the swing.
In the backswing, when the club is horizontal to the ground, it should be pointing straight back at the camera and from there the takeaway should continue to a higher position.
Then from the top, this should allow you to come into the ball from this higher position, taking the club back down through a similar position when parallel to the ground, and, more importantly, fully extend the right arm into impact whilst maintaining your height and spine angle. From this, you should get to wanted to achieve in the first place - higher hands at the finish - but rather you should have been able to get there as a logical progression of preceeding swing elements rather than trying to manufacture it somewhat.
I also had a bent left leg at impact - part of the whole problem - so I've been working on trying to have this straighter at impact and making more hip turn towards the target.
Like I mentioned at the outset, this is based on my working on something very similar with my pro but we did look at my swing on video as well as some stills of various pros at similar positions for (a rather shameful) comparisson.
As a practise drill, I stand at address with the club parallel to the ground and pointing straight back behind me (the hands/wrists already 'cocked' if you like). Starting the swing from here takes me back in a straighter line rather than too inside and gets me into that higher position I need to be at the top of the swing. Then I can attack the ball with good arm extension at impact rather than dipping down and bending the arms.
I have to say it's taken a while to get this going over the last couple of months, trying to unlearn years of mistakes from a self-taught swing. One of many bad habits unfortunately.
To start with I was struggling with it - making a few thins, struggling to keep my weight on the front foot and even coming over the top a little. However, as it's improved, I'm definitely hitting the ball better and with more control. When it really comes together, it's brilliant but still a way to go, though.
Hope that helps a bit. Like I said, this advice is on the basis of something similar I've been trying to change in my own swing that has been too flat, too far on the inside in the takeaway and too 'armsy' through impact.
Caveat (!): I've tried to sound objective above rather than too perfectionist and the paraphrased words of John Jacobs ring in my ears - 'as long as the swing is repetitive...'