Hi @Alobdell89,
Thanks for being patient with me while I looked into this issue!
I had a look at your design, and found that I was able to easily reproduce this behavior! However, I also noticed that you have a large amount of Move features in your timeline with no Snapshots. As the design sits right now, Fusion is just having a bit of a hard time keeping track of the positions all the bodies in your designs.In a parametric environment, positions matter a great deal because when computing the design (Ctrl+B), Fusion 360 redoes everything that you did in that design in the order that you did it!
However, it seems like this design might be more suited for a direct modeling environment. In a direct modeling environment positions do not matter as much - where ever the bodies/components sit is where they are and Fusion doesn't really keep track of it. I show this in the screencast linked here, where I switch to a direct modeling environment (making Fusion "forget" about the positioning of the bodies) and attempt to do the same move, which snaps right into place.
I also think that there may be a small misunderstanding of one of the most powerful thing about Fusion - joints.
Instead of "Move"-ing the different bodies into positions, you should try creating joints between the plates (for lack of a better term) and the frame. It looks like a few rigid joints would get you exactly what you are looking for. More information on joints can be found in the links below.
Fusion 360 Learning
AU Joints Videos
I hope this helps! Please let me know if you have any questions or concerns.
Cheers,