I have experience with 4 7mm-08 rifles. In one of the 2 savage axis rifles I shoot the Hornady 139 gr Whitetail ammo is very inaccurate. Over 5 inch group at 100 yards. That rifle does prefer 120 gr SST with groups around 1.25 at 100 yds.
The other Axis accepts all weight bullets and groups under 2" at 100 yards with any bullet. I prefers heavier bullets and groups about 1/2 inch tighter with the 154 to 162 weights.
I have a savage 110 heavy barrel rifle that groups 139 gr Hornady btsp around 1/2 inch at 100 yards. I regretably sold a Steven model 200 in 7-08 that was very accurate with light weight Hornady Superformance ammunition. None of my other 7-08s prefer this ammo.
Try till you find a load and practice at distance if able. Prepare for 400 yard shots at deer or antelope in Wyoming. You may also encounter your game at 30 yards in forest.