Never load a 7-08 but...
Have loaded a lot of different 270s, 308s and 30-06s.
I'd start with Varget and If I couldn't get what I wanted there I'd move to H4350 and think on LeverEvolution and SuperPerformance. BLC-2 might be worth a think too.
I find with Barnes, that picking a starting seating depth, then work up to find the top end and if I did not have accuracy there move up to .010 off and back up .010 each trial until the groups come under an inch works best. Beginning seating depth can be completely arbitrary IMO.
I think I've done more than 40 rifles now with Barnes bullets and the only thing I know for certain is that seating depth can be very, very critical and each rifle is very much a law unto itself about what depth it wants.
Personally I would use 120 TTSXs, but that's me.