In the 1995 Precision Shooting Reloading Guide, one of the authors described a 300 Win Mag he had that just would not tune below 2 moa no matter what he did by way of component choice or load adjustments or case prep. The last thing he tried was outside turning the neck. The groups dropped to 1 moa. So, it isn't necessarily a waste of time to try it, especially if the Weatherby is to be used at long range. No guarantees, of course, but worth a try.
There was a tool made by the old Lee Manufacturing Company that held a case in a neck sizing die to align it, and had a concentric journal for a special reamer with integral shaft for the journal that you ran inside and cranked by hand to render the neck wall thickness uniform all around. It was called a Zero Error Target Lee Loader. In my opinion, the neck turning method was better than outside turning because it not only got all neck walls the same uniform thickness, but it simultaneously removed any inside donut there might be. The only thing lacking was giving you a choice of cutting depth and resulting neck thickness. But no mandrels or adjustments were required.