308 with 110 grn Hornady CX, they are intended for the 300 blackout but my 308 with 20" barrel likes them. If there are any downsides it's advantageous to not shoot critturs too close to you, probably under 75 yards as they can be explosive, the other downside is that my choice of loads means 350 yards is the point at which the energy of the bullet hits 1000 ft.lbs, slightly under at 400 yards, according to my ballistic calculator. Doesn't affect me though as my max range is 100 yards less than yours.
Barnes website has data for 110 grn 308 ttsx which you can use to start your load development, BC of the CX betters the ttsx as it has a boat tail. My 308 liked the minimum load of RL7 but the bullet has an MV of around 3000 fps. It may perform equally as well at higher velocity but for me I like it as is, less than 40 grns of powder.
My gun (Browning BLR 81) is around 7.5 pounds all up and recoil isn't an issue for this 80 year old with a rotator cuff injury on my recoil shoulder which baulks at Win 94 30/30 recoil with 170 grn factory loads
Accuracy is adequate for me.
I acquired them for the little 40 pound muntjac deer we have over here in the UK, Hornady suggests they may be adequate for up to 300 pounds, personally I'd use 130 grn tsx for larger deer like that as they carry much more energy out to 300 yards.