I suggest you draw a characteristic curve (H&D curve) for normal development and see if there is a place on it where you could place the shadow to get the change in density you want between that point and the highlight. You can get mightily confused if you try to make Zonespeak tell you everything. The toes of various films differ in the same developer, and the toe of any given film may differ with developer, so you should have at hand a family of H&D curves for the film and developer you intend to use. Maybe you will get a wider density range simply by sliding your exposure range up the scale, but maybe you will not. I would expect that placing what you call Zone 2 where Zone 4 would normally fall on the H&D curve would give you lot of excess density, especially if you must develop more anyway to get Zone 8 where you think it ought to be.
Whatever way you make the adjustment, you will not know for sure why it did or did not work unless you know the shape and speed point of the combination you used. You could, of course, try various combinations and take the one that works.