The biggest issue, as you can clearly see in the video, is that I'm doing something weird and wiggly with my upper body and then sitting up way too soon - so soon that I'm hitting the saddle over the top of the fence. Definitely a bad habit, but I'm not sure how/if it's exacerbated by riding in a dressage saddle. I would certainly prefer to ride in a jumping saddle, but finding one that fits Saga hasn't been a priority for me since we got the house. I did start out the ride in my Wintec AP, but Saga let me know right off the bat that he wasn't comfortable in it. He really pitched a fit, but all our problems miraculously went away when I switched back to the dressage saddle after 10 minutes of warm-up disaster.
The other issue is that, in two-point, I keep my hips positioned to the left. Waaaay to the left, apparently. I've known for years that my body is somewhat awkward on the left side - I tend to sleep curled left - but this is the first time someone has pointed out how it's affecting my riding. I made a big effort to shift my hips to the right, and lo and behold, Saga stopped falling in on the corners are went much straighter. It's really amazing how much our bodies affect our horses' way of going. So, something else to practice.
I would also like to point out what a SAINT my horse is - trotting and cantering to the fence without a single change of rhythm like an old pro. It's kind of odd to ride a horse that doesn't bolt to the fences, like Cash did. It's going to be hard to learn to wait for the fence, but as Paige very astutely pointed out, it's not going to run off or anything, so I can let it come to me.