Bed,float and a trigger job would be the way to go for me.
Is the rifle stringing it's groups or throwing flyers every so often?
Another question is how are you cleaning your barrel as this will affect your barrel if your looking for .5" or better groups.
If your only punching holes in paper then you've got to start looking at things like OAL of your cartridge, bullet seating length, projectile and powder selection.
With a 1:12 barrel you should be able to use up to 175gn pills and maybe try Berger's,VLD's as well.
Powder wise try Varget which is actually an Aussie powder branded here as AR2208 and it works well in the .308's here as it was originally designed as a military powder with good temperature stability and clean burning quality's.
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