AA1680 is your powder of choice for 120gr and lighter bullets.. CFE-BLK and 1680 are about a wash with 125s. CFE-BLK is better for 130gr and above, and AA1680 for 120 and below. Bill Wilson said you can't get enough CFE-BLK in the case with light bullets to overpressure it.
According to a couple sites the Ham’r case capacity is 29.6 grains while the 350 is 36.5 grains. Sizing the 350 neck down to 308 would not affect case capacity much on typical bullet seating depth” I would think. Would be a fun wildcat I think if the bolt could handle it.