The sako 123gr game head factory load worked well for me in smacking goats with my wee model seven in 308. Was not a reduced recoil load but definitely softer than a full house 150/165gr load. I shifted to a Belmont 150gr load instead for a bit more versatility.
A suppressor really is the simple answer though, they then wouldn't be limited to a certain type of ammo that could be hard to find reliably.
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