2015 version is absolutely buggy.
I found where to download the most recent 2014 version, from the Adobe Creative Cloud application (thank goodness).
It's more stable, and working correctly, for whatever reason.
Ful Responsive Scaling behaves unexpected. They did improvements with edge.6.0.0.min.js
that broke my project. I replaced it with edge.5.0.1.min.js and everything seems to be right again.
A little bit hot sewed but maybe this is an option for you to solve your problem, too.
So, I figured out what was happening.
1) Any graphics that you import into Edge Animate need to already be sized down. If you resize them in Edge Animate, well, I got unexpected results.
2) You should save out your layers one at a time, in Photoshop. DO NOT use any batch process to do this. Once the batch process graphics ended up in E.A., I ran into problems.
3) Convert anything that you want to rotate to symbols. Set your anchor point on both the stage, and inside the symbol. This will make sure that your rotate point stays consistent, from save to save.
4) This is the second time where I posted up a question, while waiting for a correct answer, troubleshot it myself, and then came back and posted the response. Maybe I have a hidden career in Adobe technical support? :-)
Thanks everyone! Happy creating!