Joe,
I'm curious why your smith doesn't feel the Remington is strong enough for the Edge. The usual "strength" reason given is the 1.062 tenon of the Remington doesn't give enough thickness for a .580 diameter case like the Rigby (.338 Lapua) or .378 Weatherby. See
http://www.riflebarrels.com/articles/custom_actions/378_weatherby_remington_700_action.htm
But the Edge is a .550 body. There shouldn't be any lug setback, and the chamber shouldn't swell beyond the elasticity of the brass with reasonable pressures. And the Edge is nothing more than a .338 RUM, a Remington offering -- it just predated it by a bit. See
http://en.wikipedia.org/wiki/.338_Edge
(maybe a hair longer, as it is a wildcat on the .300 RUM). Having said all of that, I would agree there are better choices than a Remington, but not for strength with normal pressures and a .545 body diameter case.
* * *
Here you go talking velocity again. If you're shooting known distances, the extra velocity only buys you a little advantage in wind deflection. Most of the 1,000 yard shooters I know who use the .338 have gone to the smaller cases, for accuracy reasons -- those very slow powders don't seem to give the accuracy. Or to be honest, H-1000 and VV N-170 don't. Don't believe either Steve Shelp or Scott Fletcher tried Retumbo, thought I wouldn't rule Scott out.
Scott, BTW, has been shooting .338s for over 10 years, and won some HG firsts in several IBS Nationals, including at least one Heavy Gun "overall."
You can use an Edge & H4831 with the 300 grain Berger, the case just won't be as full, and you can't run over about 2650 & stay in the 60,000 psi region. But if you're one of the lucky ones & can get your barrel to not have fliers with the very slow powders, you have them as an option.
For me, if the .338/375 Ruger doesn't work out, I'll just run our existing .338/404 reamer in a little short with the next barrel -- probably .125 short, for a case length of 2.750 instead of 2.875. Pushing the shoulder back is not hard, but also not much fun -- I've shot both the .30 MHV and SHV, which are the .404 case with the shoulder pushed back. The old neck/shoulder joint with its crease winds up in the new neck. Annoying, but with boat-tail bullets, not really a problem.
Point being I've already got all that tooling, and for anyone starting out fresh, it would be nice to avoid the cost & effort.
Anyhow, for my money, with a Remington, you're limited to the Edge or Ruger. An action with at least a 1.125 tenon & sufficient receiver-ring diameter -- a 1.250 tenon would be better still -- lets you include things up to the .338 Norma, .338 Lapua, or the .338/378 if that's your preference.
The 10-inch BAT with a nominal 2-inch diameter is perfect. That's what my rifle is built around, though the action has been cut down (shorter tenon length), with the action sides milled a bit, to lighten the action.
The BAT M153R -- an 8.5-inch action -- would work, too. See
http://www.batmachine.com/products/products.htm
FWIW