First off, congrats on posting a video and withstanding all the critique. Feedback here can sometimes be overwhelming! I'd say for a recreational skier, you're skiing quite well! Considering the short bit of hill you have to work with, you're more than equipped for it. I'm also late to the game but maybe some of the below will help.
Most of the advice above is sound (I'm not so convinced about pole length suggestion--sorry TDK, I think chilehed actually looks quite extended with pole on snow at the start of the video before his arms get raised).
Stance is a great focus for you - work stance on a mellow run at first to develop your stance. Ironically stance is the foundation of skiing, but the hardest to develop without in-person feedback. There are so many different ways to feel balanced over the foot without actually being stacked through all parts of the body! Short of taking a lesson, one thing you could do is if you see an instructor skiing around, ask them if they have a couple of minutes to show you a good stance, and place you into a functional stance. (Or you can come to Cypress and I'll do it for you.) Short of that I'd want to eliminate the piking in your waist. First off, point your elbows down rather than out. Then, on a mellow run, imagine you have a sign on your chest, and think about showing it off to everyone -- you can't show it off if you're piked over! To stay centered, you'll likely have to create some changes as suggested by the guys above, such as pulling your feet back, or driving hips forward.
While showing off your chest, do some of these exercises to develop your stance:
- a few turns way forward over the ski, a few turns way back over the ski (find your centre)
- Thousand steps (need to be able to step using the whole ski; use a really mellow run)
- shuffling turns (shuffle feet forward and back throughout the turn--for you, this will help with dorsiflexion, or flexing the ankle. If you can't shuffle the skis behind you, you could try removing the stiffener screws on your boots.)
- hop throughout turns (small hops, ensuring tips and tails both come off the snow; start hopping through the traverse to get centered; after you're strong here, then gradually hop a bit earlier as you exit the turn; continue until you can hop down fall line and eventually hop into the start of the turn)
A good barometer for your stance will be a mellow bump run. If you're piked over still, you'll definitely feel tossed around. If you flow, you're centered and mobile. (and flexing. and pivoting. and edging. and timing things well.)
I'm not sure what you're wearing around your hips (fanny pack?) but my suggestion is if you can ski without it, do so - gear tends to shift people's balance point.
Best of luck--let us know how things go for you!