Excellent call on the zone-hopping.
I confirmed that both in-mission and on streets in Dark Astoria, the counter does not increment.
However, in both First Ward and Night Ward, the counter *did* increment. So I was about to get the Chipped Talon badge.
Interestingly, I *can* make progress on the Castigator badge on the streets of DA.....
So I'll chalk this up to "random issue", appreciate the different-zone advice.