After revisiting more YouTube videos I decided to try scything. I think I found the secret to the elusive BBS shave. I started to try it on select areas like my chin and left jaw line while I shaved the rest of my face the same as I have been.
Every spot that I successfully "scythed" came out perfectly BBS with one pass, even the thick bristly whiskers on my chin. The Mach III had nothing to cut when I went back to touch up.
Now ill try this again adding more face to the scything motion tomorrow at my next session! If I can figure out good angles of attack on the rest of my face over the next several weeks I may be ok.
On another note, while performing this guillotine motion, I see what folks say about the squeegee effect. It doesn't feel like its cutting hairs at all. Feels more like "wiping" them off my face. I seriously couldn't feel it cutting anything. At first I had to feel to see if it cut any hair but that's when I found it left only perfectly smooth skin! So far this guy is a happy camper and although my neck is once again a bit raw from my traditional methods, I'll try scything it tomorrow and post results.