The 35 gr. FBHP Berger and the 39 gr. Sierra BlitzKing seem to work well with the 1 in 12 factory twist barrels. However, some shooters have problems with bullet stability out of their 1 in 12 twist barrels when using the 40 gr. V-Max. I had good luck with the 40 gr. Nosler BT bullets out of my 1 in 12 twist factory barrel on my Savage 12VLP in .204 Ruger.
In my experience the 35 gr. FBHP Berger is a fine bullet for predators and saving fur. The BC of this bullet is fairly low, but if you keep the distance of your shots down to 200 yards and don't have much wind, the 35 gr. Berger is one fine bullet. I've never used it much for prairie dogs because my load is a hot one and not a good one to use in warmer temperatures.
I also use 39 gr. Sierra BlitzKings for coyotes and prairie dogs. The BC of the 39 gr. SBK is quite high and bucks the wind and shoots very flat out well beyond the capability of the 35 gr. Berger. I have had good results on coyotes and haven't had much fur damage with this bullet. It turns prairie dogs inside out and they do fantastic acrobatics when hit right.
I haven't shot many coyotes with the 40 gr. V-Max, but those that I did shoot wound up with some fairly large holes in their hides. The 40 gr. V-Max has been a great bullet for prairie dogs for me out of my Savage 12VLP .204 Ruger with a 1 in 11 twist stainless steel super match grade 3 groove Pac-Nor barrel.