The muzzle brake MUST be solidly locked...either in the fully open or fully closed position and cannot move if it is to function properly. The brake hole is only a few thousands, 0.010" to 0.040" larger than bullet diameter and any movement could cause the bullet to touch the brake on exit just slightly and it doesn't take much to open a group.
The brake hole MUST also be parallel to the boreline otherwise gas blowing through different size gaps around the bullet will affect the exit, tipping it slightly and opening groups.
Opening and closing the brake will also affect the barrel vibrations at the point of bullet exit and affect bullet grouping.
Does the brake move around when locked in the open position...you didn't mention that.
You could also just accept the grouping as long as it isn't a pattern. You didn't say what size the Savage group or your groups were. Are we talking the size of a pie plate or 3-4"?
One question I have is WHY did you buy a rifle with recoil you couldn't handle. My first thought would be to get rid of the rifle and buy one with a recoil you can handle...that would solve the problem. If the Savage people found no problem then it could be a subconscious problem on your part, looking at it objectively, no derision intended or implied.
You could also have a gunsmith remove the Savage brake and install a solidly mounted muzzle brake or MagnaPort it.
It also depends on the game you are hunting...again you didn't specify. A 300 WM is a bit of overkill for deer, even the larger ones(arguably) and shot placement is much more important than a huge boomer, so a 7mm-08,308, 338 Fed, 358 W or similar calibers on the '06 case, might be your cup of tea and would reduce the recoil level 25-40%. Maybe a 7mm RM if you think you need a magnum. It has plenty of pizzazz for NA game and recoils about half way between an '06 and a 300 WM.
There are several ways to mitigate recoil by adding a good recoil pad, using one of the new spring loaded shock absorbing stocks, installing mercury weights and/or just adding extra weight to the stock and fore end. A heavier rifle will reduce the recoil level.
If you are hunting something large and mean and cant' handle the 300 WM without a brake then you might be overextending your capabilities and should rethink your position. The 300 recoil is about 15-25% more than a '06 and shouldn't be much of a problem if you learn to shoot it and shoot it enough to learn to handle the slap.
Last but not least and probably the cheapest way to go is to down load to a lower power level, lock the brake one way or the other and forget it. The 300 WM responds well to reduced loads and I think there are factory reduced loads available, although I'm not certain.
I have a 300 WM barrel for my Savage LA with mag bolthead and I've loaded it down to 300 Savage levels just for kicks, to see how the groups were. From 300 Sav to full house 300 WM, it will keep 1" 3 shot groups all day long as long as I do my part.
My "sage" advice is to buy a rifle you can handle well, use accurate ammo and work on the fundamentals of good shooting...then don't shoot anything beyond your capabilities. There are lots of ways to solve your problem...pick one or several and be happy.