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cold trigger:
I want to stick with standard Ruger brass.

Hornady is standard 375Ruger brass. Hornady Basic 375 Ruger is the same brass but without the shoulder-neck sizing.

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My recommendation is the .375 Ruger.

My wife went that route because of Tanzanian law. I doubt if there is much difference between .338" and .375" on an animal, but yes, a bigger hole probably helps in 2% of the cases.

For up close and personal. Wider is better! But a 300 gr 338 and a 3oo gr 375 bullet at the same velocity are going to have very similar effect on game. :
For me the big differences are bullet availability and long range ballistic coeffeficency.
If I was going to Africa then the 375 would be the automatic choice, I'm not so that isn't part of my equation.
When I shot the 338 alot I pretty much ALWAYS wanted the velocity of the 340 Weatherby. I was still in Southeast when I sold my 338 RUM . When I had it I didn't feel the need for more velocity. I was pushing 275 gr bullets at 2850 fps. That rifle was a M 700 so that's why I sold it. I replaced it with a 375 Ruger Alaskan and had the exact same amount of confidence in it on up close brown bear problems . Not I'm wanting more of a long range round and as I already have all the components except the reamer for the 338/375. It seems I could get 340 velocity or close to it from the Ruger action.
I hadn't taken into consideration the CEB bullets or the GSC bullets for the 375 . So I'll have to think some more.

There are some very high BC bullets from CEB for .338" but they require single feeding. Their 1.1" nose profile will not fit in a Ruger magazine. On the positive side, a super long range bullet is a single-feed affair anyway. Lower BC bullets can be in the magazine for upclose bears.

Since some of the technical side is beyond my non mathematical mind.
I ordered the 338/375 Ruger reamer with .3" more freebore than the 338 RCM has. That will give me the ability to safely long load the 300 gr bullets.
If I need to single load them for lr shooting that's ok for this first rifle.
I've looked at the Richardson and Roberts action. One of their receivers has a 3.6+" mag length so that would hold the 300 gr CEB bullets in the mag.