If you want a 7600 pump their is nothing wrong with that, they are excellent rifles and while they maybe can't be tweaked like a bolt, the ones I have owned all shoot very well. However bare in mind the size and weight of a 7600 will enhance felt recoil/blast. I have owned 308, 3006 and still own 270 7600, the 270 & 3006 were pretty close in both aspects and IMO I felt the recoil more than similar chambered bolt rifles I owned. That would leave you with 243 and 308 to choose from, personally for my area the 308 win would be the choice hands down. However if you found the 3030 to cover all your needs than either may work fine and offer range improvement as well.

I now only use bolt myself,main reason is fit, second is accuracy obtained, third is simplicity of design & finally better shooting technique. I have found their is no reason to worry about the follow up shot b/c I make the first one count with my bolt & should theneed arise I can recycle the bolt fast enough for a more accurate follow up in any regard. If you consider a bolt the choice is much higher for what yourasking. I agree eitherthe 7mm 08 and 2506 would fit the bill grandly.