Well, despite the TE website listing nothing under 'Compatible Parts,' they actually responded to an email inquiry and answered my question: 583259-4 is the compatible terminal. (However, it only accommodates wires up to 20 AWG, so if any of the experts here can point me towards a compatible "Modified Fork" terminal that accommodates bigger wires, it'd be much appreciated.)
Yes, it is definitely a PCB edge connector, specifically AMP 926108 (unknown dash number). I initially didn't upload a photo of the back side (shown on the TE website), but here you go:
It seems the the bigger-gauge terminal I need is 583362-7 (or possibly 583363-?), but I can't seem to find anyone selling them in quantities of less than 6000! Does anyone know where I can get just one or two (or 10 or 50, frankly, if that's what it takes? (Or, alternatively, as Ian suggests above, an entirely different six-pin .156" pitch edge connector for .063" thick mating edge??)