DING DING!!! We have a winner!! IMR-4350 is a great choice.
I've loaded it for several 7RM and 30-06 rifles with great success. I'm sure that it would be great in the 7-08 as well!
It may not give the fastest velocities in those calibers, but for a one powder to do it all, it would be hard to beat. RL19 may be the next best choice.