For 150gr and above, mine likes the Berger 150gr Classic Hunter, and my wife's love the 162 Amax. In my experience I would avoid bonded bullets at 7mm-08 speeds. 150gr Ballistic Tip is a great bullet for this cartridge as well.
ThisThe 7-08 is a very capable round with the right load . With a short barrel and heavier bullets there going to be slow . There's not enough case capacity to really get them moving. If you went copper mono like a barns ttsx you could come down on weight and they hit hard . I'm currently pushing a ttsx 140 at 3055 with 51.3 gr staball6.5 and the 120 will do 3260 at 53 gr . Now I'm running them thru a 26 inch brux and you will loose some due to the short barrel.