Dan,
I do a lot of the crush grind pepper mills... I usually have a dozen or more in stock at any one time in my booth. Everyone will have their own method of doing them, but here is how I work them.... I buy the $10+/- bits at Woodcraft most of the time... I only use 3 sizes in my mills, even though the directions will indicate 4...
I use a 1 3/4 at the very bottom, then drill through with the 1 9/16... this is the hole the mechanism fits into and also holds the supply of pepper corns... the third size I use is the 15/16 in the top for the little white part that holds and turns the shaft.... The directions will tell you that the through hold has to be 1 1/16 and the white top piece will fit inside and act as a tenon... I find that this allows too much movement side to side in the top, so I don't use the 1 1/16 drill bit, but cut a 1 1/2 to 1 17/32 tenon about 3/8 inches long that fits inside the through hole and stabilizes the top.
I use the cheaper forstner bits with an extension for the 1 9/16 bit to drill all the way through... drill slowly and back out often so as to not overheat the bit. The cheaper bits from Woodcraft will last for a dozen or so mills and I have sharpened them on my 1 inch belt sander and gotten a little more use from them, but even the more expensive bits will go dull after about a dozen mills, so I think it's more economical to use the lesser priced bits... my opinion, not set in fact...
After I have drilled the holes, I have a recess tool, (It's one I had when i was trying to learn to chase threads that is used to recess the wood at the end of the threads...)... I use that to cut a groove inside the top and body of the mills to accept the little fingers on the top of the mechanism... some directions will tell you to cut them away, but if you can put the groove in place, the fingers act as a compression spring and have a small hook that will fit into the groove and prevent the mechanism from being pulled out.
Second step after I drill the holes, I set the top aside and turn the body... some turners will put the two pieces back together with the top piece in place and turn the mill as a single piece... I don't like to do that myself, I prefer to turn the as separate pieces. I use a jam chuck that is tapped and threads onto my headstock spindle, then I have a turned jam chuck that will fit in the 1 3/4" hole at the bottom. Turning is pretty much free form, what ever your design is. Once you have it shaped and sanded to your liking, lay it aside and do the top...
I have a set of pin jaws that fits my PSI Barracuda chuck that fits inside the hold on the top piece... I put the top on them and move the tailstock up to hold until I'm almost done with the top... I then move it back and cut away the little tenon left where I hold it with the TS.... this is just a safety measure I use... I've had a few not hold on the pin jaws because I either didn't tighten them in the hole enough or I got too tight and split the wood, so I just snug them up and use the tailstock... most of my tops are rounded balls....
Most of my designs are relatively simple without a lot of beads or coves. The round top I try to size to look pleasing in conjunction with the size of the body.
On the through drill, if you're uncomfortable drilling all the way through or are worried that you might break out the top when the bits exits the wood, then the practice of switching ends and drill half way is a good practice... on longer mills, I have to do that as my extension is only about 9 inches.... btw, make sure your extension is pretty hefty... they will wobble and wander just a little, especially as your drill bit dulls.
All this said, Ed Brown has a very good tutorial that he did on turning pepper mills... and I think there are a couple of others on YouTube.
