My two cents:
The back cast is not terrible-The loop is reasonably compact, and it appears that you are applying speed with the lower hand. Two things that I think could be improved on the back cast are; 1. You are lifting the elbow to shoulder height after you make the back cast, but prior to the forward cast. This puts you in the position of casting downwards on the forward cast. 2. It appears that the tip of the rod is traveling downwards at the end of the back cast. To my way of thinking, this means that the eloop must follow.
The forward cast is another thing entirely. The apparent lack of acceleration at the end of the fore cast is giving you a gigantic loop. The downwards path of the rod tip, ( Due in part to the high elbow,) is probably sending the cast down into the water. It also appears as though you are overpowering the cast terribly, and making the entire forward cast with the upper hand, the lower hand merely being along for the ride.
In summation, I would concentrate on:
1. Keeping the tip as level as possible throughout the casting stroke.
2. Taking advantage of the leverage afforded by the two-handed grip and applying the speed to the cast with the lower hand at approximately the same time that you would normally double-haul with a single-handed cast.
3. Not overpowering the cast. Good casts come from good technique which doesn't have a lot to do with power.
4. Throwing tighter loops on both the fore and back casts.
Lastly I would say that I think you would be better suited learning with a WF line rather than a braided mono shooting line. Shooting heads and braided mono lines will go a mile even with mediocre technique.