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I was thinking if something like this would work?
If you're trying to choose between buying a router base or a drill press, I would buy a drill press first. I use the drill press way more than the dremel router base. (Unless you think you're going to be getting into fancy inlay work.)
For this project, any 6mm drill bit will work for the round MOP inlays. The bottom doesn't necessarily have to be flat. Just press them in and put a little thin super glue around the edges and let it soak in. Or use epoxy. They will never come back out.
And like Don says - a little high is better than a little low. You can practice on a scrap piece of wood to get the right depth worked out beforehand.