For what it is worth my experience has been to sight in from a rest or bag. Even that contains several variables.
Example : Staccato XL at 15 yards with SRO dot off walker bag on bench. Hornady American Gunner HP 124g +p.
Achieved sub 1.5" groups 5 rounds , multiple in same hole. WWB 115g fmj was comparable.
Now, Remove the bench and bag from the equation.
The 124 +p stayed tight but the WWB 115g fmj was better for me.
My point Is try different ammo, be sure technique is as best it can be before you start bumping the important parts of your gun around.