Basically what I was thinking, though with a 15" dowel, the DP chuck is likely to get in the way of dowel changing from the top. If they were shorter, the drill the 2" hole, insert 3/8 bit, start drilling dowels is a great way to keep things centered.
Now your second post is the real "duh!" moment. Simple, accurate, easy, no-brainer, (shall I go on?). Perfect!