As shootforfun and XTR say, it's hard to get velocities up to competitive levels. Bear in mind that the better 140gn 6.5s have the same G7 BCs as the 168gn Berger VLD and that in turn has a considerably higher BC than the 168gn Sierra MK (0.316 v 0.289, source Bryan Litz). IME it is much easier to get the 260 Rem / 6.5mm Creedmoor to give 140s MVs above 2,800 fps (in a 30-inch barrel) with good accuracy than to achieve the same performance with the 7-08 and the Berger 168. (That's with a long-throat chamber too which sees the bullet seated at 2.96" COAL.)
The 308 Win based case is really a bit short of capacity for 7mm in the long-range target role. 284 Win in long-throat form is a much better competition cartridge for mid and long range.
If you want to really push MVs in the 7-08 with heavier bullets, you need to go to double-based or high-energy powders, both of which incorporate nitroglycerin making them denser and also increasing their specific energy ratings. So, we're talking powders like Alliant Re17, Viht N550 and N560, Ramshot Hunter, Hodgdon H414 and suchlike. The cost of using these powders is two-fold: greater temperature sensitivity; hotter burning which reduces barrel life.
As a nice, accurate short/mid-range cartridge, there is nothing at all wrong with the 7mm-08 paired with the 168gn Sierra MK. It is pleasant to shoot and gives longer barrel life than the mid size 6.5s, but it is ballistically challenged compared to equivalent 6.5s and sixes. In the hunting role, it's at its best with 140-150gn bullets - there are no factory rounds with anything heavier than 140gn bullets last time I looked.
The 4350 / 4831s' burning rates are very well suited to the cartridge with heavier bullets, but you can't stuff enough of them in to get full pressures and velocities. So, you generally need something like H. VarGet, IMR-4320, Re15. IMR-4350 can be used at a pinch (with a compressed charge), H414 or Ramshot Hunter (for hotter burning loads with higher MVs). Some 7-08 shooters like IMR-4007 ssc, but this powder was withdrawn a year or two back - there may still be some tubs in the shops as it wasn't a big seller.