Was just about to post the same thing about going to a 6.5 of some kind but you beat me to it.
Barring that, the starting loads of 4895, either IMR or H, should be very accurate and turn the .30-06 into a .300 Savage or even less.
FWIW, I use 46.0 IMR4895 as a standard target/plinking load with Hornady 150 grainers and it has proven extremely accurate across all four ought sixes it has been used in. And if that recoil is a bit much you can even go lower and should be able to maintain good accuracy.
