Hi, Doghouse.
When ya turn the thin, wide stuff, you have to account for both varying flex on tool contact due to change in grain direction, and for change in shape due to release in tension of the wood. A good way to do this is to turn the outside edge when there is still some meat to the piece. Once it is turned, ya just gotta leave it alone.
You can make minor modifications by bracing it with your hand behind where the tool is hitting but this will hurt if you blow the piece up and won't work once the piece is out of round due to tension release. Make sure and wear a glove when doing this.
The other option is sanding. Don't press on one side without bracing on the other. This will help keep it even. You can also wrap the sandpaper around and do the inside and outside of the edge together by pinching it. This is my preferred method because it works well maintaining consistant thickness with slight out of round.
Past that, beautiful work!
Welcome to the world of non spindles!
Dietrich