It fit!
As usual, the timberturners come through. Again, I appreciate all the replies and the great information- will file it for future reference! To back up a bit, I turned the wood between centers and turned a tenon on one end. I put the tenon in a three jaw chuck and drilled to 5/16 (should have gone a bit bigger) and then put it on a 5/16 mandrel between the Jacobs chuck and live center. Turned to dimensions. But, as I said, I got impatient with hand reaming and drilled with the insert in one hand and the drill in the other. Duh! Doesn't work!! Put that on list of things-not-to-do. I fussed and fumed over it. Forum friends came to the rescue. I finally discovered I could use a hand lathe to ream to a good round shape and the ID I needed. Hand lathe, you ask? It's a wood rasp in the left hand and the insert in the right hand. I got the ends to the proper ID/wall thickness. Then I turned the insert with the right hand while operating the rasp in the other, using the parallel part to clean up the inside. When it looked good with the one-eye inspection tool, I put it on the rod blank. Eureka! It fit! I'll commit to posting pictures of the finished turned insert and turned custom grip. Again, thanks! BTW, the rod is for my grandson.
Hockenberry, thanks for that tip. I'm going to try and make some tree ornaments for the holidays. Need to get started.
My son can have some mandrels made from drill rod in various diameters. Shoulder on one end and drilled on the other end for the live center. This will make this much easier than lots of reaming.