I think you'd be better off working a little harder with your subjects to move them away from the backgrounds. The 24-70/f2.8 is not really that different than the 85/f1.8 - basically it's a trivial amount longer and one stop faster. DOF changes from about 8 inches to about 3 inches by going from 70/f2.8 to 85/1.8 - and that even assumes the old standards for 8x10" prints being "large." The 105/f2.8 is about the same as the 85/f1.8, trading longer focal length for slower aperture.
I don't think you really want to change lenses just to get this relatively small advantage.
You might find the 135/f2 a bigger difference (I certainly do), especially if you choose to use the DC option, although that needs to be used with some real care. Unfortunately both it and the 105/f2 AF DC are both well more than the 105/f2.8, so likely well out of your intended budget.
_____ Brian... a bicoastal Nikonian and Team Member
My gallery is online. Comments and critique welcomed any time!