I would neck up 30/06 brass, that is NEW.
Winchester will suffice, or New Match Grade Lake City if you could find any as it is really tough.
Necking up is less likely to create doughnuts than necking down, and I can not stress this enough.
To check for doughnuts forming at the shoulder neck junction, after firing, simply push a bullet down past the shoulder neck junction...easy peasy!
If you have already acquired dies, neck up some new 30/06 brass, measure the dia of the neck with the bullet seated. Now, get the reamer dimension on the neck from the gunsmith. If he does not have a print, he can do more than a WAG off of measuring the reamer flutes. By doing this, you know if you need to neck turn.
Necking up 30/06 brass will produce thinner necks than necking down 35 Whelen brass, and will possibly eliminate the neck turning, worth a shot?
If the gunsmith is still working on the chambering, they always have to cut off an inch of the muzzle. Have him run the reamer into the depth of the shoulder. If you have this simple tool, you can use it for several things, including checking if the necks are too thick by simply dropping the loaded round into the Piece of Muzzle Stubb, that we used to call, " neck Checkers".
I fire form my 280 AI cases with 15g of bullseye, then fill the case full of cream of wheat, put a piece of paper towel in the neck to hold it all in. My cases are formed 97% on the first firing with the cream of wheat, where they shoot exceptional groups. You could copy this if you are so inclined.