Here's one of my segmented goblets. Red oak, padauk, black walnut, yellow heart and purple heart. Finished with Michaels's Triple thick. Comments welcomed.
I will post a pic of it glued up and that will pretty much give you the general idea. The center I always use a different wood than any of the rest of it is made of. In the pic the pieces are 1/2" x 1/2" and the length has to be long enough for the chuck to grab and be able to cut it off. My finished goblets are anywhere fro 7" to 8" tall. If your going to drink out of it I would recommend 5/8" x5/8" pieces so you don't have to fill it up as often. The most important part is to make sure you get it dead center when turning or it throws every thing off. I use a razor knife to mark my x in the center. I forgot to mention it is wrapped with 3/4" wood. The pics I have here are a different goblet but it gives you the general Idea. I would love to see somebody else make these. Every body who sees them loves them.
I do pepper mills that way with relatively good success... have only tried it with a goblet once some years back with mixed success... I like what you've done... really elegant looking pieces.