Tyson, ditto what dogcatching is saying, the cross hatched cut lines do not have to be perfect. The two lines can be cut with either a thin blade bandsaw, scroll saw, or chuck mandrel in a vise and cut with a fine tooth metal cutting hacksaw or even coping saw. I use a hacksaw for a lot of things such as this. Spine mass of hacksaws prevent vibration and cuts without snagging in hardwoods.
Run your cuts down about 1.5" so you have enough flex without the segments breaking off.
BUT....all that said....I really, really like what dogcatcher is advising. Delrin plastic might be the order of the day for you. Its reasonable cheap, readily available on ebay, inert and as he said your finishes would not bond as readily to as they will to the wood. GREAT idea.
to You Dogcatcher....hadn't really considered, although I use it in the shop in other capacities...lol.