The muzzle brake argument is fine, I personally don't like them, because they are super loud, and suppressors are pretty expensive, but that's just me.
When I first got interested in LR I was against MB's. I shot a 300 RUM Sendero for a few years without a brake and I was OK with it. I usually had a slip on recoil pad on it which made it very tolerable. After reading a lot of threads and posts in here and actually shooting a braked rifle, I decided a brake would be very useful and make shooting much more enjoyable. The noise wasn't really a factor because I wear hearing protection anyway.
On your other points though, are you pushing a 230 out of the RUM anywhere near 3000 fps? If you are, and you are going to use a brake, hell yeah bigger bullets going faster are better. Just go with a 375 AM and call it a day!
I expect to push the 230's @ about 3150-3200 fps out of a 27" barrel using RL33. This thread was comparing a 7 RM to the 300 RUM. If we were comparing the 300 RUM to the 375 AM, the 375 AM is of course going to be a better LR rifle.
Second, what magazine box are you using and what is your COAL that fits without the any more than the boat-tail being seated below the shoulder / neck junction? Just so that we are all on the same page.
When I first started this build it was throated for another bullet. It was built on a 700 action. The 230 is seated about .100 into the case and it fits into a 3.82 mag box. I am loosing a grain or so capacity with that configuration. 3.99 mag boxes are available so it is possible to get more efficient and seating max case capacity with 230.