I have long used the Sierra 85-grain HPBT for all-around shooting in my .243. I won't use it for larger deer; just in the 90 to 125-pound (field-dressed) central Texas whitetail range...
I have had very good groups from the Federal ammo that uses this bullet.
My favorite handloads are the 85 with 37.5 grains of 3031 (start at 36.0 grains and work up.) and the 60-grain Hornady with 40.0 grains of 3031 (Start at 38.0...). My groups run 3/8" to 1/2", generally.
You might check the bedding on your rifle. My opinion is that the barrel should not touch the wood of the fore-end of the stock. After I free-float a barrel by removing wood from the channel of the fore-end, I then shim with wax paper out at the tip. A 1/2" strip, folded back and forth until the thickness requires about a five-pound pull to put it in place, works well. Trim with a razor. Shoot several quick shots to heat the wax so it will stick...
Good luck, Art