To make the Corian insert this is how I do it.
I use a scratch awl to draw an X from corner to corner. Then make a nice dimple in the center. Next put some double stick tape on the other side of it and put the dimple on the point of the live center and bring it up snug to the spindle. The tape and tailstock has plenty of grip to turn with. Now just turn it round, I use a parting tool and run it in from the face and its round in a few seconds. Size it (I use a scraper) and make sure the sides are square to the faces. That will minimize glue lines around the edges. You should be able to take the tailstock away if you want to face off the blank but its really not neccesary.
For shakers use something like the long point of a skew to make a line around the blank so you can easily locate your holes. I use the center and the earlier scribed lines (intersection of the circle and X) to make 5 holes (1/16" is what the other shakers in the house had). I scribed a few lines around it to see what the best spacing was and that wouldn't hit the shoulder inside that the blank sits on. The shoulder is created from a 1" through hole, which fits the rubber bungs from CSUSA, and the 1 1/2" bore for the inlay. Don't drill your bore so deep that you bury the inlay other wise you will have to do a lot of reshaping of the wood after you glue the corian in. Good thing is the center hole is perfectly aligned with the tailstock so you can use it with worrying about damaging the top of you shaker. You only have to be careful when turning the very top since you will have to have the TS pulled away. I probably have 1/4" on the edges and 3/8" on the top of the corian.