One powder for all wouldn't give you great performance in all of them. I
agree with MSUICEMAN's concept to lump the '06 and 270 together plus
I'd add the 300 WM in too as Win 760 powder is a good choice for all
three calibers. I prefer ball powders over stick or flake because I load in a progressive press so H4895, IMR 4895, Varget, and 4064 wouldn't be my preference. As a ball powder, Win 760 is a good choice for all three calibers because it's more accurate in the large cases than say, Win 748 (also a ball powder and a good choice for 150grn M1 Garand and M1A loads).
This is because Win 760 was formulated for the large cases like the '06, 270, and 300WM so that you can fill them with more powder per round to gain higher velocities and achieve a higher case density. (Higher case density is one of the keys to higher accuracy in your loads. ) E.g., for a '06 with 150grn bullet, max load is 48grns of Win 748 vs 60grns of Win 760, however, Win 760 does produce some 160-180fps more velocities.
Your .223 powder choice could then be H-335, BLC(2), or Win 748. That way you are down to only 2 powders. Note: Win 760 is not a good powder for shooting in a M1 Garand as
it's higher pressure curve can bend the op rod. So, if your '06 is a
Garand, then I'd suggest H-335, BLC(2), or Win 748 for both the '06 and
the .223. You're still at only 2 powders.