And one other thing, if you were to describe exactly my stroke, is it pronating or supinating on the backswing? And also how could you tell this is a wta style fh?
I took a look at your side-view video clip, and I realized I misread what you did in your stroke. I wasn't really paying attention how your racquet face was rotating in your takeback. Usually when the racquet face opens toward the back fence, that is a sign of a WTA-style stroke. But, through most of your takeback, you're pronating your forearm, and I wasn't looking for that.
The stuff on the unit turn and footwork still stands. But it looks like you're really really close to getting the slingshot takeback down. I'm actually excited about this!
What's correct
1) For this stroke, your front shoulder is correctly above the back shoulder. The height of the non-hitting arm is correct.
2) The way you set your racquet tip at unit turn is correct.
3) At height of takeback, everything looks good.
4) You're correctly pronating after you've reached the height of takeback.
The issue:
Even though you're correctly pronating your forearm after the height of takeback, you're actually supinating too quickly and you're actively straightening out the arm. Due to both factors, when you reach full extension, your racquet face is now open to the back fence, and your wrist is very laid back. Because of that position, you find yourself supinating -- while still in your takeback -- to scoop your arm out of that position, so that you can initiate your forward swing. If you tried initiating your forward swing while still in this position, your hitting arm would not open up correctly.
Solution:
This turns out to be really easy to fix.
Once you've reached the height of takeback . . .
1) Let gravity drop the racquet and finish taking the racquet back, just as you would do in a normal FH stroke.
2) Pronate the forearm slowly until you initiate the forward swing. You pronate continously until the end of takeback, but you do "just enough." From the height of takeback to the end of takeback, you may end up only supinating your forearm about 20 or so degrees.
3) Completely ignore the arm. Don't intentionally straighten the arm. Let the arm relax. You will find that when you do steps 1 + 2, the arm will do "its thing." Don't be concerned with whether the arm straightens or not. As soon as you do, it'll disrupt the flow of the takeback.
4) It helps to visualize the racquet tip still pointing between right side fence and net, as the racquet falls. This can help make initiating the forward swing easier.