Warning about the generic Hornady 416 New Dimension, seating dies. I reload a wildcat made from 375 Ruger virgin brass cases. I have a set of Lyman 416 Rigby F.L. dies, and it works with trimming the sizer back .300". The seater works right out of the orange box. I also have a set of custom wildcat Hornady New Dimension reloading dies. Both seating dies leave my undersized cases unsupported at the shoulders. Too much crimping can and does buckle my shoulders.
My Ruger parent cases are much tougher than many of the Rigby ones. I have the complete case forming set to size down from the Ruger Basic Brass. I just run a loaded (buckled) round through one form die to iron out the buckled shoulders. Now I run every loaded round through it just to make sure they will all chamber.
With the different Rigby brass cases being what they are, I would suggest staying with the older RCBS, ect. sets of reloading dies. These support the shoulders much better than do the Hornady New Dimension variety. You may not notice this, but my custom chamber and reloading dies are so close, that any bulging or buckling will stop a round from chambering. I designed in the very same half inch long neck, as the factory 416 Rigby. This is why I can do most, but not all of the reloading process with the Lyman dies, made for the larger diameter Rigby's. I can't full Length resize, but only neck size, expand, seat, and crimp, with my Lyman dies.
My custom New Dimension Hornady wildcat dies, do full length resize, but their generic sleeved seater, by definition, can't fully support any of the .416 family of case shoulders. I hope that making you aware of this problem will prevent it from biting you, in the future.
Remember that with the large tough bullets in a .416, you can't effectively run a loaded and crimped round back through your F.L. sizing die, to iron out buckled shoulders. With my forming die which only touches the tapered case bodies, it is a snap. This die has a faux neck, which is about 11mm, to hold the necks against the hack saw blades. It is also a file trim die. So I run the cases through my .416 F.L. die, and then after I crimp the bullets in, I run every loaded round back through this taper only forming die. After firing, there is no visible bump at the case head, body junction. Any problems with the buckled shoulders are negated by the accuracy of the sleeve, in seating those bullets, inline. One other concern is that the preferred Lyman dies have a bare few thousandth's, step up to the expanding button. The Hornady New Dimension dies have elliptical expander buttons, and will deal with dented case mouths, and such.