Asking for help from the 'experts' again....

I have purchased a couple of sound hole medallions from Folkcraft for a teardrop dulcimer I am working on.  My question is do you attempt to use a fly cutter or hole cutter to make the medallion flush top with the dulcimer top, or do you simply glue it on raised above the dulcimer top? The medallions are 2 3/16" diameter so, for me anyway, it means flycutter; as I don't have that size hole cutter.  And flycutter means sandwiching the top between two pieces of thin scrap to avoid tearing the hole in the dulcimer top piece.  All said, it would seem to me flush is the most appropriate way from a design perspective and pride in craftsmanship.