sometimes a self bow looks center shot, ,but the limbs are configured so it is not shooting like that,, or it looks center shot at brace but does really not line up like that,, at some point you have to believe how the bow is shooting,, or not shooting,,
if you look at Native American bows,, you can see,, center shot bows were not needed,, I have some bows where the string is toward the arrow side that are pretty close,,I did read Badger say he shot a bow that had the string alignment off to the side, and it shot well for distance,, so I think there is a sweet spot on every bow were the arrow shoots best,, sometimes upside down,,
I usually take my best practice arrow,, and put a head on it for shooting at a deer,,
20 to 25 yards is a long shot for me,, I have killed deer out there,, but if they jump or flinch you will not hit where you were aiming,,
if I was going to shoot a stone head,, I would put masking tape on it to keep it sharp and shoot it into something soft,, worn out hay bale or something,,