Honestly I have no idea whether leaving a continuous perimeter or tabs would work better, I’d do a small test piece and try it out (or hopefully somebody who already knows might tell us ;- )
What you could consider is machining it with a mm or two of excess on the bottom side, flipping it upside down, putting it in an MDF jig (Shapeoko out a negative) and then surfacing the topside down to final dimension if the Z dimension and face need to be accurate?
My main concern is the remaining strength of the wood, especially in the cross-grain direction once it’s cut this thin.