20 October 2020
My answer is you don't need a bigger mandrel at all. Just back off the collet die until the neck is the size you need for your bullet. If your case neck thicknesses don't vary more than .001" this will work fine. Most good quality brass will meet this requirement. I know this isn't according to Lee's instructions but there is no good reason to have extremely consistent case neck IDs.
If the loaded cast bullet round chambers freely just enough tension to keep the bullet from falling out or being pushed back in while in your pocket will do. If you are pressing the bullet into the throat or want clear land marks on the nose of a bore rider, you can determine how much is enough by trying dummy rounds so a round can be chambered without pushing the bullet back in the case. Of course you can't try different case neck IDs if you are pressing the neck down on a mandrel unless you has a set of mandrels of different sizes -- so it is sort of a catch 22.
The danger of seating anything but very hard bullets in a too small neck ID is damage to the bullets by lead shaving, upsetting to inconsistent diameter or even bending a long bullet. Are you sure you are getting away with seating .310/20:1 bullets in a .305 neck without damaging the bullet?
For more information read my article "In Praise of the Lee Collet Die" in the July/August 2020 Fouling Shot.