I've loaded bulk 110g .30 SP projectiles designed for M1 Cargine loadings in .308 Win. I use a fairly fast rifle powder and load them to max M1 carbine speeds, so there should be no stabilization issues at any reasonable range (say 100 to 200 yds). The cartridge profile is a little wonky, so fast feeding from the magazine might be an issue, but they work great.
Because the recoil is so light compared to the heavier projectile loadings, your zero will likely be substantially different, so you'll have that to deal with. Muzzle blast is reduced, which also helps with new shooters too.
.308 Win reduced recoil loading I used:
110g Rem .30 SP
24.3g IMR 4227
LOA 2.400"
chrono avg velocity 2152 ft/sec
Derived from Speer #11 (1987) and Speed #12 (1994 )starting load data for .308 Win.
They used 25g for a velocity of 2121 ft/sec
This is just bulky enough (1.9cc of powder) that double charging should be detectable, which is not the case for loadings using pistol powders like Unique or Red Dot would be in such a case. Empty case volume with that projectile will be around 3.1cc
You can use a 110g .30 cal FMJ too. I used the softpoints because I also use them in a .30-30 reduced loading in a tubular magazine.