Well I put all of my changes (even TransformGroup changes) in Behaviors and had some troubles. I tried making them update every frame, but then they didn’t draw frames smoothly because I guess they had no reason to redraw otherwise so animations didn’t work out. So then I made them work every 1 millisecond just to see if it’d work. That was fast and better for animations but some frames got skipped and objects would flicker out of the scene sometimes. So things still weren’t in correct synch. Then I moved the TransformGroup changes OUT of the behaviors, and made my Behaviors update on TransformGroup changes (sure glad I found that option). Now things are working much better. I have some kinks in the system still but I’m continuing the work so hopefully I’ll get things working like I want to soon.
However, all of my Behavior work has had absolutely no effect on the original problem. I even tried not updating the Box’s behavior (when the Shape is still empty) and when that happened the lines drew properly. As soon as I updated the behavior, the Box was added to the scene and the sporadic lines immediately disappeared 
Off to LineStripArray I go. While it’ll lose the ability to have broken lines when I WANT to, I’m hopeful that it’ll at least solve this problem. Maybe I’ll learn new things with it. It’s worth a shot. That’s the last suggestion you made that I haven’t tried yet. I’ll tell you how it goes when I’m done.
I also see I can use it to definite separate strips so I can have breaks when I want to. I’ll have to learn about that when the time comes. Thank you for jumping through all of these hoops with me. Although I still don’t know what caused the original problem I’m glad to know I’m at least able to work around it and move on 