I did finally resolve this issue, so I wanted to report. Based upon the info from the Mark Levinson people, further consultation with others, and taking resistance and continuity readings from the various pins of the various ports, I decided to wire up the new cables with the shields connected at both ends. The units work/sound great, so I did not bother to try any other shielding configurations.
So, to review, I used Lemo connectors, size FGG.1B.305.CLAD52 for the five pin ports, and FGG.1B.302.CLAD52 for the two pin ports. "CLAD52" refers to the outer diameter of the cable, so you will need to check that one and adjust accordingly depending on what cable you use. I used shielded cable, with the shields connected to the housing of the connectors at both ends.
So, to review, I used Lemo connectors, size FGG.1B.305.CLAD52 for the five pin ports, and FGG.1B.302.CLAD52 for the two pin ports. "CLAD52" refers to the outer diameter of the cable, so you will need to check that one and adjust accordingly depending on what cable you use. I used shielded cable, with the shields connected to the housing of the connectors at both ends.