Hi, Lee!
Several articles from the American Rifleman, Rifle Magazine, and others have established that a bullet with long-nose bearing surface that rides on the lands is best for cast bullet accuracy in .30 caliber cases. The .308 Winchester is slightly handicapped with it's short case neck, but can still give fine cast bullet accuracy. MOA is more often than not the result.
The first one that comes to mind is the RN Lyman 310291 at 170 grains, the similar 150 grain, and the various copies of this mold from Lee, RCBS, Lachmiller, etc. Cast from linotype, sized to .309" with gascheck, lubricated with Alox, and loaded over 9.0-10.0 grains of Unique, this gives fine plinking accuracy in .30-06 and .308 Winchester. It's also my favorite in the .30-30, .30-40 Krag, and .300 Savage. Powder charge may vary for best accuracy, and recoil is very mild.
"Midrange" loads use medium-fast IMR 3031, IMR 4064, or IMR 4895 in moderate charges of 35-40 grains. This last one is a favorite of service rifle shooters when they don't want to put up with the recoil and noise and expense of full loads.
I've found that the pointy "spitzer" type cast bullets usually do not shoot as well as the RN bore-riding types. I would avoid full-power loads and jacketed bullet velocities for best results.
All of these loads of course, should be verified in the Lyman Cast Bullet Handbook.