Some really good advice on chucks. Once you have something that is easily adjusted or easily adjustable, you won't want to go to a non adjustable chuck.
Another option is to mount a chuck to a face plate, and have 3 or 4 blocks with a fine thread for adjustment in the blocks. Depending on the amount of offsetting that is required. I like to use M5 or #10-32 as they are a fairly fine pitch thread. I like using 4 adjusters with 2 keys. So it is like setting a 4 jaw but you are moving the chuck body over.
On my setups, I have sets of bellville washers that keep pressure on the chuck to the faceplate, and the 4 blocks can move the chuck body around no trouble. I have about +- 0.5mm on mine. More than enough to centralise any piece at any size on the self centering 4 jaw. I also have a Grip true chuck which is my main chuck on my little Myford lathe. It's good as the chuck itself is very repeatable. So when set at a size and the stock is round, it does not require adjusting to have parts run true. By true within 0.01mm on a dial indicator. When things need to be set better than that,it requires adjusting of course.
The only issue with self centering 4 and 6 jaw chucks is the out of round stock issue. To get around that, I usually place the 0.25mm or 0.010 inch ,card between the chuck and the part. The card will crush at the higher contact points and less so at the lower points. Another option is to use the 0.010 inch plastic shim instead of the card paper.
It also over time will help to make the equipment last longer.
Neil