Take that junk stock and give it to somebody you don't like,with a smile and a handshake.Go straight to your local gunshop,and order a HS Precision stock with all the bells and whistles in the varmint style.
This will negate all the debate about floating your barrel,it will be done by the stock for you.
You may have to special order the inlet size for your barrel,if it isn't a heavy barrel.
If you can't order the correct size inlet,you may have to settle for the sporter style,but there's nothing wrong with those anyway,still has aluminium bedding block,floated barrel and nice semi flat fore end for bipod use.
I think the effective range of the 30-06 is somewhat less than 1000 yds,unless you use a projectile like the J-36 ,we must remember that TARGET bullets are exactly for that purpose,TARGETS.
Also,you need to use a bullet with high BC,something like the Nosler 200gr Accubond,BC .588,and I don't think the 30-06 can push it fast enough for that range.So I would keep my shots inside 650 yds just because you don't want wounded game on your conscience.
Good Luck with whatever you decide!