I've had the same problem and went about solving it in a different way, as I had some serious demands on the accuracy of my ammo.
I had Lee send me a set of their .003" oversized dies, both full length and factory crimp.
The problem as I saw it was that the cases were being oversized. The reason is that there are wildly wide tolerances in case thickness with the myriad of manufacturers making 9mm brass. In order for 99%+ to work after run through "run of the mill" dies, it's neccessary for them to make them a bit on the "tight" side. Back in the '70's, it was common for die manufacturers to put notices that their dies may not give sufficient neck tension with some makes of brass, usually good American mfg. brass!
Not to mention this (lop-sidedness) plays hob with the accuracy, particularily with the "run-out" you're seeing.
By using Federal brass, I'm avoiding what I see as a problem with the Winchester brass having as much as .002" variation in neck thickness, and very shallow primer pockets. Actually, I had even worse luck with the Remington, especially some I bought new/unprimed.
I now get very low runouts, very good accuracy and no high primers.
Still, don't overly flare the necks; Just like Jim Watson said, just enough to seat the bullet w/o shaving the bullet or collapsing the case, and then a minimal taper crimp with the Factory crimp die, which will "erase" a small bit of runout by "pushing" in the side protruding, but won't correct the amount that I've seen occasionally come out before the die treatment.
Before I got the O/S dies, I would back off the sizer die approx. 3/4 turn, which eliminated some of the "Coke Bottle" effect from excessive sizing.
Your firearm will dictate to some extent what you need to do. My S&W Perf. CTR 9mm Auto's made it real clear when things weren't to their liking.
Yes, with BlueDot, you'll see essentially "full" cases of powder with the 9mm. Some data I've seen and tried would not fit in the 9mm brass I tried it with. For easier measuring, try either Win.SuperFld, AA#5, HS6, or Win231. I couldn't get the accuracy or velocity with TiteGroup before the pressures got too high. Might work better for you, though. Best 9mm reload accuracy I've gotten was with 4.9-5.0gr of Win231 and 115gr JHP, at 1.125" oal. Followed very closely by 5.3gr of Win SuperFld.