How to handle batch processing tasks?

Not sure what coasters you’re using that aren’t the same size. I use slate coasters from Amazon and use a jig that I can load 20 at a time on my Omtech C02. By the nature of the slate coasters the edges are chipped away, so I don’t try to engrave all the way to the edge. The sizes of the coasters are consistent enough to work in my jig. On the slate coasters I use nobody would be able to tell by eye if the design was off center by a mm.
Perhaps you’re doing a different type of coaster and exact placement of the design to the tenth of a mm is necessary.

I’m guessing log splices (or more like tree branch slices)… if so, or similar, how about a template that has circles(?) that fit the largest expected workpiece. Then you only need to align your pieces inside a small shape, which would be easier to do by eye. You could even have crosshairs in the templates around the workpieces.

Circles like a target with numbers along the cross that’s what I usually do.