When I learned (last summer) it took me a long time to learn how to get up, so hopefully you can learn from my experiance.
When you're in the water and just about to go your skis should be as close to vertical (up and down) as you can get them. Don't struggle to get them up like that, just relax and float. But you should at a minimum be past a 45 deg angle. More is better.
The start description is kind of what threw me, a "sitting" position. Its more like you're sitting (knees at a 90 deg angle) but your shoulders are touching your knees. You want to get your body as far forward as you can of the water will just beat you back down. Imagine sitting in a chair and touching the floor between your feet.
Don't pull or fight the rope. You should maintain the "sitting" position until you are going, which shouldn't take long. If you are still dragging in the water after 5 second, let go of the rope because you aren't getting up. Once the skis have gone from vertical to horizontal then simply unbend from the waist. Leave you knees as they are. (OK, you can unbend them a little from 90 deg.

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Once you are up and going DON'T BEND YOUR ELBOWS!! All this will do is put slack in the rope. When the slack pulls out you will get pulled off your skis.
That's all I can think of for now.