Hi Justin,
Here are a few things to consider. KingPin mentioned that your slide foot is not in your center of gravity, which is one thing. There are probably a few things causing this.
I tried to evaluate your video a little and here are a few things to work on. Your non-throwing arm is doing nothing. Have a look at some good bowlers or PBA pros, you'll find that the other arm plays a role in balance. Kind of like a tight rope walker, always uses 2 arms outstretched to balance themselves.
If you pause the video at your delivery, you will find your whole upper body shifted to the right. That makes it very difficult to be balanced...and have leverage. Your head should be just to the right of your slight foot.
Watch this video of the 2009 US Open.
http://www.youtube.com/watch?v=l_eHiHDbQLI At around 2:30, you will see one of my favorite deliveries from Richie Wolfe.
A couple of things to highlight:
1. watch what his non-bowling arm does. It will be equal and opposite of the non-bowling arm, i.e., the higher your back swing is, the lower the opposite arm is, and vice versa. But it is more or less stretched out.
2. Watch where his head is in relation to his slide foot. It's just slightly to the left (he's a lefty). So you're spine should be a little more aligned.
I won't go as far as to make it straight up and down as this is more from the classic days.
3. One of my favorite parts is what his back leg is doing. Watch how he keeps it outstretched and on the ground. He is perfectly balanced. This is some thing I suggest do look at.
Of course, if you have a coach, you will certainly get differing opinions so you need to trust what you're coach is trying to teach you. This is hopefully supplemental and not in conflict.
You can also have a look at my article and coaching video exactly about this topic of leverage, upper body vs lower body.
http://tamerbowling.com/index.php/where-do-you-get-leverage-from/ Good Luck!
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www.TamerBowling.com USBC Certified Level I