OK. Short answer to the original question: the 4-pin AMS Lite cable IS NOT a standard Molex 4-pin - For whatever reason, BL assigns the pins on both ends in a non-standard way.
How do I know? The 4-pin Molex cable, when installed, ended up on the printer and the AMS Lite not connecting after handshake, whereas the original BL cable (which I got two weeks+ after I started my search 
) does indeed work.
Question solved.