Trigger time and I mean LOTS of trigger time and truthfully it doesn't need to all be with the selected elk hunting rifle.
I am on my 4th 300Win Mag as I recall, a couple were questionable at best due to quality issues and a couple, one of which I passed on to a son, were great. My current 300 is a RUGER Hawkeye which is a VERY accurate rifle and one that also produces higher then expected velocities.
I spend a lot of time at the bench developing loads for one rifle or another, with the goal of developing an "optimum" load - one load/one bullet - for each hunting rifle, and knowing that some folk will not agree, I think that great amounts of trigger time on the bench and off go to improving your shooting abilities.
Probably 40years back, I allowed a post 64 Winchester 300 to hurt me during rushed load development and I was just never at home with that rifle again. It was also one of the defective 300s I have owned, the other a Browning "A" bolt that while the smoothest actioned rifle I've ever owned had a barrel that looked like it had had a threading tap run down the length of it.
Anyway, after that damaging experience with that first 300 I just made it a point to not allow a rifle to hurt me or at least not enough to develop bad shooting habits.
As said, I spend a lot of time on the bench and for many years have used a sand bag or sissy bag between the butt of the rifle and my shoulder when shooting much of anything above a .243. This includes MUCH load testing/development time with a 45/70 and heavy cast bullets.
Forget that terrible idea of a muzzle break! If your so much in a rush to get off a second shot, it is highly likely you rushed the first shot. DON'T!!!!!!!!!!!
I'm NOT suggesting that you use a bullet of 165gr in a 300 as I think a 180 or 200gr is a much better choice, but after the Browning experience and trying a bunch of different bullet/powder combinations in an attempt to get consistency and good groups, - I never did - I had a bunch of 165gr Nosler Partitions on hand and have gone on to use that bullet, with success.
The 200gr Nosler Partition was the bullet of choice in the RUGER #1 - 300 that I passed on to a son.
I WOULD NOT feel ok with that choice were it not for the fact that the Partition is high in integrity, the point being that what ever bullet you select, make it a good one with proven integrity. The cost of the best bullets available is very small when compared to the other costs of rifle, scope, hunting an camping equipment and the expense of just getting to your hunting location.
Your possible suggestion of buying a new rifle and having it barreled is off the wall. Just buy a good rifle and forget all the other misdirected thoughts your friends have fed you.
My RUGER Hawkeye is giving me sub inch groups at a muzzle velocity of 3318fps with the 165gr Nosler and I'd expect it to also give excellent accuracy with a more proper 180 or 200gr bullet.
Trigger time even with a .22 rimfire, you need lots of it!
Crusty Deary Ol'Coot