Well, those numbers sound small. I have no idea what 0.001-0.004" on that gage means.
IOW, does your rifle chamber hold the tip and base?
I ask because on my rifle, the bolt face pushes the case body taper and case shoulder taper into mating tapers in the chamber. My case base diameter really doesn't change from fired to sized more than a few 0.0001's. So, I consider the base as a datum and the body/shoulder surface as formed by the die as a datum. When spun, this shows me the cartridge centerline as it fits in the chamber. Then, I want to know if the tip of my bullet, well actually about 0.1" back from the tip is pointed. Is it aligned with the case axis, or a couple 0.001's misaligned? That is what drove my purchase.
That said, the Hornady tool may work very well. I just cannot determine from its design, if it will be helpful. I returned mine.
I also tried straightening ammo. That was a cluster! I think some made a right turn exiting the muzzle! I made a 0.5"-0.75" AR shoot 1.5" groups!
Good luck with your new tool. Hope it gets you where you want to go.