It could work but there are several limitations that make a 338 Lapua based 7mm a much better choice.
First off, you will need bullet weight and barrel length to make it work and the slowest powders you can get your hands on. I use WC872 in my 7mm AM. I have used Retumbo, H-50BMG, AA8700, H-870, US869 and WC872 and I always come back to WC872.
Bullets, you want at LEAST 180 gr of bullet weight and you will be much better off with a 200 gr bullet like the great ones from WIldcat Bullets.
One problem with a 7mm based on the 30-378, the brass is VERY soft. I would be suprised if my 7mm AM would not match or even possibly exceed what a 7mm-378 could produce with same bullet weights and same length barrels.
The reason is because the Lapua case will handle dramatically higher chamber pressures then the norma made 30-378 case. Even though the big wby has a capacity advantage, it is overshadowed by the fact it can not use that capacity in the 65,000 to 68,000 psi chamber pressure range and get more then a couple firings off each case.
On the other hand, I have pushed the hell out of my 7mm AM finding the designs performance limits, I have yet to loosen a primer pocket on a Lapua case.
Also, the 338 Lapua based rounds are sigingicantly shorter in OAL and will be easier to git into a repeating rifle. I use the HS Precision DM system and it works perfectly well even with the 200 gr ULD RBBTs.
I get a comfortable 3300 fps in a 30" barrel with the 200 gr ULD RBBT. I could horse it up to 3350 easily and possibly even push 3400 fps but there is no need to push pressures that high.
BB's 34" 7mm AM will easily top 3400 fps with comfortable loads so that shows the potential of the 338 Lapua case when necked down to 7mm and used with HEAVY bullets and ultra slow powders.
All this performance does come at a cost. IF you shoot in wide temp ranges, you will have to develope the load for the hot temps and live with the velocity drop in cooler temps. Also, these class of 7mm rounds can be a bit finicky to some degree, the heavy the bullet you use, the less this is a factor.
If it were me, I would look at the 338 Lapua case as a parent case over the 30-378. Its just a much better start to your project.
Kirby Allen(50)