Re: How is this for a vertical string
You were taught wrong for a weapon with recoil . Anything using 71.5 grains of powder has some recoil and you can't shoot it like a BR gun with lighter recoil and expect to control anything . Watch film footage of Military snipers shooting long range stuff and no one I have ever seen does that and I was not taught to do that in the Military with only the 308W to contend with.
Stop listening to BR competition shooters who never fire anything bigger than a 6mm PPC or similar .
A rear sand bag , as in a cloth bag filled with sand is a poor rear rest and will only support the heel of the stock and butt plate / pad most of the time and it will just dig it's way down into the bag with recoil . Make sure you remove any sling studs from the rear and from the forend if not using a bi-pod . See how much guessing I have to do when I can't actually see what you are using .
If using a leather or cordura rear bunny or rabbit ear rear bag and calling it a sand bag then that is much better .
I think in part the gun is controlling you not you controlling it .
No single style suits all gun , cartridge , stock combinations and I have two guns in the same cartridge firing the identical load and they like slightly different handling techniques , probably due to different stocks , triggers and barrel weights . However with any gun with recoil you have to start by controlling it and go from there.
If you are waiting for the barrel to get to hot to hold onto then at that point it would be way to hot during the shooting session.
At this point you should stick to three shot groups , shoot slowly and watch the wind and don't let the barrel heat much at all. Firing five shot groups is a waste of ammo until you work out the bugs . When you can put three in a tight group consistantly then shoot bigger groups if you want . For a hunting rifle the most important shot is the first one from a cold barrel not the 5th or 10th shot in 99% of cases.
So work out a load that gets the first cold barrel shot in the same place each time , zero the scope and then practice with that load to get the next two shots close by . If you can do that consistanly that is all you need for hunting.
However you also have to be aware that the POI zero at the range off a bench may be different to how the gun shoots in the field on the dirt in a prone position . So once you feel you have it sorted out test the gun in the same position and way that you will shoot at game to the best you can that is , as you can't cover every possible situation .
You may find you get better results laying behind the gun rather than sitting at a bench .