easiest and best looking would be from the bottom. you don't have to worry about getting the hole you route out too big etc.
dont rout out too much though, you still want some wood for the screws you'll mount it with to have something to bite into., also if it's too thin, and you risk making it weak or having screws poke out the top when you ount.
i would route out 3 or 4 mm to start and try it out. install the stick, the overlay, plastic (if you are using them) and see how it sits. if you need a little more height on your stick, take off another mm or 2. but be warned you can always take off more, but you can't put it back.