I get your frustration. The shapeoko is a great machine, but if you want a perfect machine then be prepared to spend double or triple the money.
I do not move anything once I start an epoxy inlay cut.
It doesn’t take much to be off by .03".
Here is how I would do this project.
Carve all the Epoxy pockets at one time. Pour the first color into every pocket. Let cure for at least 24 hours. DO NOT MOVE THE PIECE.
Go back and recarve the next color to remove the epoxy. Pour the Second color. Let cure for 24 hours.
Then finish all the remaining toolpaths.
Remove the piece.
I have one project that I do epoxy inlays on and this is how I do it.
Most likely the machine is fine. Unless you are using an anchor point (1/4 Dowel Drilled in 2-4 spots through the piece and into the spoil board) you are likely not putting the piece EXACTLY back where it went. I recently had an issue with SawDust being on my fence. It wasn’t much but it threw off the whole piece. A minor bit of interference on the far side of the piece will be amplified.
This is not mine but you get the idea.