Time for another update! I put the servos in it and tested it out. Sadly, it didn't work very well. The big ring (on the outside that gets moved around by the servos) rotates slightly when I try and move it in one direction or another. After a few times moving it, the ring rotates too much and gets caught on the "sliders" that hold it onto the green cross pieces. Then, the servos makes strained noises, it can't move, and (I thought this was cool) it heats up the green color change filament to a yellow color around it. I'm thinking that maybe adding a bigger bevel/chamfer onto the friction points of the sliders/ring would help, but I'm not sure. Hmmm... I have to figure out some other way to vector the ring around. I'm also having trouble adapting the 5mm motor shaft to the 1/8in gear ID. I tried printing out an adapter (you can see it in the picture), but it turns out that an 1/8 wide cone of 3D printed ABS isn't very strong, who would have thought!
Oh, and here's a link for the Onshape project:
link Not sure if anyone here uses Onshape or is interested in the files, but you're free to look around if you are!