This is getting pretty close to a solution for hunting. I have been shooting pigs with hollow point 175 gn cast bullets in .30-30, MV about 2200 fps, and I'm talking a couple of thousand or more, not just one a few years ago. I have found both the velocity and the hollow point necessary for consistent results on hogs. You can make your bullets into HP with a Forster hollow pointer, although mine come straight from the mould. For a soft alloy you will need to drill out about 6 gns of metal. For a harder alloy like I use, a bit on the hard side of #2, a 10 gn hollow has worked well.
In my Ruger .308 I have run the hard 175 gn bullet up to 2400 fps with 4350. It shot well at 50 metres, but groups opened at 100 metres, I believe on account of the 10" twist. Your .308 may have a 12" twist and thus handle the 2000 fps plus loads better.
I recently ran some comparisons of hard HP, soft HP and soft solid bullets on pigs, after using just the hard HPs for years. This was with 2100 - 2200 fps loads in .30-30. The writeups are on the Cast Bullet Association Forum in the Hunting section.
https://forum.castbulletassoc.org/ca...-cast-bullets/
Having never shot a deer, I have no idea how this might translate for your situation.
Most of my shooting is inside 100 meters, 150 at a pinch.