Top of the morning to you sir, I hope it's as bright and clear in your part of the PNW as it is here just across the medicine line this morning.
With the understanding that a lot of my experience is with old school powders and in some cases from rifles we fooled with 30 years ago, I'd say this about that.
A long passed on shooting and handloading mentor was what I believe John Barsness called a "rifle churner" in that he'd buy, sell and trade constantly. That said it did mean we got to play with different stuff and run it across the chronograph "for the sake of science".
During that time I put together a pair of .308 Norma rifles and fooled with another couple rifles chambered for that round. Then I picked up a No. 1 in .300 Win Mag which had a nice long throat and 26" barrel so we could get the most possible out of the cartridge. Buddy the rifle trader had examples of .300 H&H, .300 WSM and .300 Weatherby that we played with over that time too.
As a broad statement there wasn't much difference between them all and it seemed somewhat dependent on barrel length as far as velocities went, the longer ones usually getting more speed. Usually..
On deer/black bear sized game we never saw any noticeable difference on the animal's reaction to being hit between say the .308 Norma or the .300 Win Mag. The velocity/trajectory was close enough that I just held on the same place in those pre-rangefinder days.
For the life of me I can't recall if he had a Model 70 or a Remington 700 in .300 Weatherby, but I don't recall any feeding issues with it, which I do with an early Savage 110 in .300 WSM for instance.
It likely would be cheaper to buy than to build as you note and up here factory chambered rifles are usually easier to move than something custom, even if it's put together by a known builder.
Speaking of that, a local gunsmith who also has a long range shooting school and does some competition shoots a .30-.338 Improved for his competition rifle. His is built on a 700 action and he said he chose the cartridge because he was able to get very consistent velocities with a minimum of effort with that chambering. Easier than a .300 Win Mag if I'm remembering correctly.
Anyways sir, I'm not sure that's useful or not, but either one is a fine round as long as it feeds nicely in the rifle.
Good luck with the project whichever way you decide and all the best.