Ive messed about with the old 30-30 and various levels of loads. Downloading the 30-30 with a 90-110/115gr. cast bullet and enough powder to get 32-20 velocity gave me similar performance, but not quite the accuracy, though not bad. Because of the larger case capacity of the 30-30 I used top 32-20 data to get the velo. The 110gr. jacketed or half-jacket bullets would do well also. You can do the same in your .308.
Moving up, the 30-30 .308" dia bullets at 30-30 velo's in a .308 should shoot very well and for top loads you already have those available.
For super light plinkers you could even use roundball loads for 'gallery' practice loads.
All have different point of impact because of velo and bullet weight, but given a low dropping load and another target paper below your aiming bull you still get a group on paper (or move up closer). Ive even considered having another scope ready and Zero'ed for a given load to be able to pop on; say one scope -0-ed for your full house hunting 308 load and another -0-'ed for the 32-20 equivalent fun/small game/varmint load. That way no need to readjust the scope and loose the -0- for the other load.