My lathe operation for inserts is very functional and a little different than what I see others doing on the forum. If a person wishes to spend lees than a chuck clamping system this works great and is centered.
I have started using a bottle mandrel threaded on to the lathe chuck.
I predrill my wood blanks to either .375 or .3125. Then the blank is put onto a all thread rod of that diameter. I hold the blank in place with threaded nylon 1.00" x .375" or .3125 "nuts" that I make. Then I use a .375 to .375 threaded adaptor or .375 to .3125 threaded nylon 1.00 adaptor to thread to the mandrel. This way the all thread is now "attached" to the lathe. I use a free floating drill chuck on the other end.