No my quads are not sore and never have gotten sore. I honestly disagree with being in the back seat. It might look like that from this POV camera and the fact that I am 6'5".
Perhaps you're in good shape and have skied so much in the backseat that your muscles are used to it. I understand the viewpoint of the POV makes you look more in the backseat than you really are. This is because it's much lower than normal viewing height....so your height should actually make this look LESS like you're in the backseat, not more. Absorption of any bumps makes it worse because the knees come up to the chest. So I fully understand that the camera exaggerates how much and how often you're in the backseat. Trying to take that into consideration, I still think you're in the back. 3rd party video would obviously help clarify (your previous 3rd party video showed you were in the back though).
The proof is in the falls. Watch your falls..your ski tips come flying up and you "wheelie". I'm not saying you're falling because of being in the backseat...but your falls show that you are in the backseat. It's inevitable sometimes, but it shows that you don't have the natural body movements to get you out of the backseat when you get there.
1:31 - you go over a hump and fall on your butt
1:35 - 1:40 - your tips never engage the snow...in fact even in this light powder, the entire front of your skis are always above the snow...this should not happen. Beginning of the turn, the skis should dive into the snow a bit, then pop out at the end of the turn. With a chest mounted camera and dynamic skiing..I would expect to see very little ski tip at the beginning of a turn and a lot of ski tip/knees at the end of the turn. This section (along with many others) shows fairly static skiing.
1:42 - you hit a bump and go flying...your ski tips are way up in the air.
1:48-1:53 - again, your tips are constantly in the air. Every small bump you hit sends your tips flying. You have 0 control and the result is that you were not able to steer around the small tree.
4:45 is a classic case where your tails are caught and you can't turn..resulting in a snowplow move to slow down followed by lifting the inside ski to get parallel again.
A lot of your turns look like throwing your tails out to turn. This sort of turning encourages weighting the back of the skis. A few of your falls in the soft stuff is the direct result of trying to turn like this. It allows your edges to get caught going sideways rather than the skis pointing in the direction of travel.
Overall, it does look like you're having fun and that's what it's all about. There is definitely room to improve if you want. But you'll have to stop discounting what people tell you.