A Few things;
Anyone would struggle to get TIR off sized 30-06Win as low as seen from shorter & better designed cartridges. I would think consistently near 5thou would be about as good as you'll get -without more work than it's worth.
That is, your runout can't be expected to be as low as typical with something like a 6BR.
When you say "checked the case neck run-out on several resized brass" could you be more specific?
Were you checking only neck thickness, or overall case runout off the necks?
When your case TIR as measured off the necks on FIRED & UNSIZED is 2thou, well that is the very best you're going to get no matter what. This because, there is no good method to REDUCE case runout from there, other than re-firing in a chamber.
Dies only increase runout, and bending loaded necks is no good for anything we do.
Also without neck turning, or culling by thickness variance, you leave a contributing abstract to this. So if you don't do these things, to reduce runout, why bother measuring and worrying about runout?
There are improvements for your tool mentioned here:RCBS