One trick is to use the gun itself as a 'jig' to hold the grips. The frame with the grips secured into place is held in a secure & padded vice on the mill or drill table and set up precisely to the spot. If the grips are fitted properly, the horn is supported from behind by the frame so it won't flex or crack it. The grip won't move, turn or spin on the frame. If the grips are not fitted properly on the frame, it should be done so now with epoxy(!) if not only for this operation but to preserve them in one piece once the shooting and handling starts.
An end mill is my choice to make the cut. I touch up the cutting edge to leave a very slight scoring edge on the outside edges to avoid any chipping. (Same idea as a forstner(sp) bit in wood) Slow feed, fairly high speed for the cut. Even with all that there is always the possibility of chipping. Like wood, it's a natural material and it has a grain and flaws and those things can happen.
A mill is best with the mechanical feed to control it but in the very least, set a depth control so you don't zoom right through it. Thinning the medallion is a good idea on thin grips,,, just looking at the face of it anyway. No real need for the post either, just glue it into place when done. With all that said, if the grips don't fit all that well to begin with, perhaps they could be used on another gun with better results, made into service style N frame grips, knocked down to K frame dimensions, or be refitted on another N frame that is being refinished and the frame can be filed to the grips for a perfect fit. The laminate idea is a good one too. These are all of course if the owner isn't happy with the fit in the first place!