I'm likely not the person to be stepping in here.
KT, I don't remember what twist rate your ordered your barrel in, or if you posted it.
Last fall my neighbor came over with his Vanguard series 2, with a new barrel, chambered in 300 Win Mag. The kicker was he ordered a 1-12 twist and he wanted to shoot long for weight 190 grain VLD bullets.
He's a pretty fair shot and had a 1-12 twist on his 308 Win and since it shoots so well, felt the twist rate would work in his 300 WM.
It appears that he didn't correlate the differences between the lighter/shorter bullets he was shooting or felt the extra velocity generated by the 300 WM would push it fast enough to stabilize the bullet.
He finally ended up shooting 180 grain SPBTHP bullets using 80 grains of RL 22.
KT, I know that you are fully aware of which twist rate will work for the bullet you intend to shoot.
I don't shoot cartridges such as the 300WM as a matter of choice. Simply because I'm recoil shy. When I do, I use a sissy pad or a Lead sled.
I'm also sure that you know your limitations and flinch isn't an issue.
My preference would have been IMR7828ssc. Still, there is a good chance you may need just a bit more velocity, with a shorter pressure curve to settle down your bullets.
Instead of going to IMR7828, think about RL22.
I was having a similar issue with a 7mmRM. Usually H1000 with 160 grain bullets gives the best overall performance. Several shooters I know use it exclusively for all weights starting at 139 grain on up.
When I switched to a max load of RL 22, the rifle settled right down and produced very decent groups. The rifle is a Winchester Mod 70, from the mid nineties.
I wouldn't have considered going to RL22, but a good friend and mentor, explained how the the shorter pressure curve would sometimes settle negative harmonics in the barrel.
If that doesn't work, would you consider a bit of upward pressure by installing a pad at the same point the sling is mounted???? Doesn't have to be permanent. Not my favorite choice but it does work on some rifles.