Barrel legnth is required for only one reason. In order to achieve max velocity before the bullet leaves the barrel.
Anything beyond that length is unnecessary. As a rule with heavy bullets such as the .375, fewer powders are best suited,
which are of the slower burning variety. A number of years back, Dan Lilja of Lilja barrels conducted a test by starting out
with a very long barrel, and shortening it as I recall by 1 inch at a time. My memory also says it was a 338x416 improved
cartridge with 300 gr bullets. Also, years ago you wouldn't get proper velocity from a 30x378 unless you had a long barrel
of 34 to 36 inches. To make matters worse, almost nobody made barrels longer than 30". The ones I had were made by
Bill Wiseman in TX. who primarily made test barrels. Today however things seem to have changed regarding barrel length.
Powder formulas are no doubt responsible for that.
About 15 years ago, my brother in law had Bruce Baer build him a 338x416 with a 38" barrel on a Bat action.
His M V using a pretty much max load of H50BMG is slightly over 3000 fps. That case, which is beltless with a
standard type shoulder, has the same capacity as does the 378 Weatherby case.
About 3 years ago my son had Bruce build him a 338x378 wby on a large 3 lug Saco action with a 30" varmit taper barrel.
Theres about 50' per second difference in velocity between the 2 guns using 300 gr bullets.
In hindsite, I wish we had used a 32" on my sons gun, but Bruce assured us that 30" was enough and any more was just added weight.
He also tried to convince me that 30" was enough on my Big Baer, which is his version of the Chey Tac, and based off the 505 Gibbs case.
His cases are custom made for him with his headstamp on them. He uses the same case for the 338, the 375, and also a 35 caliber version which
he claims is the best of all for long range shooting.
Cutting Edge makes the bullets for him or anybody else wanting them of coarse and i believe they are 325 grain.
Heres a guy who has been building, competing, and hunting with these type guns for several decades.
A phone call would certainly be a wise investment of your time.
Another good source would be Dan Smitco at Cutting Edge bullets.