I've gotta add another vote to the 7mm/300 chambering.
There are so many great reports of this cartridge it's hard to fault. Also, there are many great smiths who post here, i'm *sure* one could get a 7/300 tack-driver all set up for you.
It looks like you have a .30cal hammer in the .30/378 so that's another good reason for a 'middle' caliber.
After using a 300 Win for a few years (plus my 7RM), i've really come to appreciate the 7mm. My 7RM ADL anchored a mid-sized whitetail for me at 520 years ago and i thought going bigger (to 300 WIN) would be better bringing even more hammer to the game. However, i found i never really needed the extra horsepower and sold my 300 WIN....
Bryan Litz wrote an article on 7mm vs .308 right here
. It's a great read and has helped my thinking/planning a lot.
Like you, I'm also planning a build and trying to decide btw simply updating my current Rem700 in 7RM or splashing out and buying a donor action, re-barreling and going with the 7mm/300. I have 300+ new Winchester 300WM brass cases so i could be reloading for a lonnnng time w/o buying brass (a convenient savings in this day and age).
Honestly, you have some great horse-power in the stall right now, but it's always fun to add another!