Try IMR 4895, starting at 36 grains and work up. If your rifle doesn't like that (I'd be surprised) then try BL-C2 and do the same.
220's DO work in a .308, so long as your rifle can stabilize them, and the only way to know is to try.
Berger also has load data for their 210gr VLD in .308 win, with about ten different powder types, and their bullet is LONG!
Kind of surprised how quick some guys are to jump on the "You can't do that..." bandwagon!