I think rather than drill balls, you drill shapes.
Therefore, it's important to mix symmetrical and asymmetrical balls and layouts to get what you want.
For instance, take the Quantum Bias, Physix and Axiom (I'm assuming you have the solid): You probably should not drill all three, because there is going to be a good chance for shape overlap between the QB and Physix. I have the QB and both Axioms, solid and pearl, and a teammate has the Physix. What I like most about my QB (I have two, actually) is the ease in which surface changes can change the shape. I think my QBs are both a bit more versatile than my teammate's Physix. Either, though, is a good pairing with the Axiom, which is a big-engined sym that offers surprising amount of shape and traction no matter how the surface is prepped.
I would then put a Phaze II under that, and then you need to get an asym pearl in the bag. That sort of locks you into a Halo Pearl, although the Black Widow B/G is a pearl-leaning hybrid. Both are big cores, though, and you may end up with a hole in the bag below this before you get into my last two recommendations, which would hands-down be the Hy-Road and the Hustle Ink going off your list.
So to recap, that's:
1) Quantum Bias
2) Axiom
3) Phaze II
4) Halo Pearl
5) Hy-Road
6) Hustle Ink
But I really think you need to consider getting an additional pearl in there. The easiest way to do it would be to swap the Ink out for something like a Phaze 4 (the Spectre would have been ideal, but oh well); you could also bench the Axiom Solid in favor of an Axiom Pearl and then take the surface on the Phaze Two down a bit and keep a close eye on its maintenance. However, the only balls I've thrown lately that can keep up with, or better my Axiom on heavy conditions where control is needed are a Motiv Forge Flare or a Storm ProMotion.