My deer hunting experience was with the .30-'06 in Far Upstate NY. Because of terrain and trees, we seldom got shots of over 150yd, and I was using a 22" Win 70 and 165SGKs. I had some success using basic 'Reduced Recoil' Remington 125gr Core-Lokts, but I also adhered to the 'not so far' shot advice that was being shared about the load at the time.
I think that shorter barrels are better suited to shorter distances, and that the heavier bullets may not be particularly advantageous at distances of only out to 200yd. I think that when we change our rifles into minimal lengths, we change their fundamental natures, and should broaden our consideration of handloading strategies. Carbine length rifles are not so similar to the traditional deer rifle. The lighter weight bullets can allow the shorter barrel to deliver them at velocities that assure greater expansion.
I did some development using the Nosler 125gr Ballistic Tip in a 22" .30BR. The Nosler 125 was a solid winner for accuracy. It's also designed for deer, probably best out of smaller cartridges like the .30-30, .30BR, and maybe the 7.62x39 in a .308 bore, and probably good for larger chamberings in carbine lengths.
My thinking is that the shorter barrel probably puts the .308 into a velocity regime closer to those smaller cartridges. I suggest the 125BT with H322, W748, or AR Comp.
I ended up working with the 125BT, 125SMK, and 135SMK and IMR-4198 in the .30BR, which is probably also another good powder. I have been using it for my 7.62x39 Savage Scout 16-ish" with 110gr V-Max and GMX. The transition to heavier 125's should not be such a large jump for me there. IMHO, such a combination could turn my Scout into a Deer rifle for brushy country.
In general, I suggest a lighter weight bullet and a faster powder.
Greg