But they are calibrated to produce the same 12-18% depending on manufacturer, which leads to different readings on the meter, and between manufacturers.

Gossen uses K=11.37, so if C=250 for a flat diffusor, we end up with a reflected gray value of about 14.3%. Other values for C exist for hemisphere diffusor, 320 is common. So using C=320, k=11.37, gray= 11.36%. The reflected percentage formaula is % reflectance for grey= pi(3.1416) x k/c. It would seem to me, that both numbers are factored to get the final reflectance value, and are dependant on each other and other mathematical gymnastics.