If you are going to use 165-168 grain bullets and heavier in the .308W either H380 or H414/W760 would work. Not a common application, but available and useful. I used H380 for years in hi-power competition in .308W with 168's; max H380 load with 165-168 is 47-48 grains in .308W. Finding any load data for H380 is difficult but data for .30-06 is printed on container for 155's and listed by Hodgdon..
Lots of .30-06 data for H414/W760. IMR 4166 is also a possibility. Win 748 is another, most bullets for .308 and 150 and lighter for .30-06. Except for the IMR4166 the powders mentioned are ball powders and fit inside the .308 W case well. I am surprised that H380 is still made; it is a popular powder for the .22-.250. Then there is the orphan IMR 4320 powder - seems like nobody likes this any more and it might be discontinued and is on sale at many LGS'.
Accurate 2520 data is listed for both .308W & .30-06; I have never used Accurate 2520.
Edit:
Way back then, IMR 4064 was sort of a classic powder for .30-06, it works very well with 150's and probably 168's and was commonly used in M1 Garand rifles. 4064 is a first rate powder for the .308W. 4064 is a good selection for both .308W & .30-06 and being an extruded powder fits inside the .30-06 case well.
I believe, H380, a ball powder, was originally designed for military .30-06 loads, probably to complement 4895. My old Speer manual indicates H380 is OK for Garand use. I have heard that current lots of H380 are slower burning than older lots.