Update: I am currently trying out some 14" K Custom Dark hi-hats and 13" K/Z hats. First impressions are that both of these are closer to what I have in mind. I may pick up some 60s or 70s New Beats at some point.
So the K Custom Dark hats seem to be working out. I think they are covering most styles, sometimes the tone is an exact match. They are a cross between the Dream Bliss and the New Beats I owned prior. If I hit them just right, I can get them to match Jabo Starks hi-hat sound in James Brown's Talking Loud and Sayin' Nothin'. My crashes don't match the tone of that song when it has a break from the groove at 2:36. My crashes seem to sound fine with the hats otherwise.
Of course, this took me down a rabbit hole because my ride didn't go well with my hats. I do have a K Custom Dark 20" ride on the way.