So converter shows 13.7 as it should disconnected except for the meter on the output. Under load the voltage drops by various amounts below what it should hold at with those loads.
So is it something to do with the MH loads or would it happen with all loads?
Since the converter is on its own like that, you can take the wires out of its output terminals and put some other wires to it with some other load that is not from the MH. See if the converter can hold its voltage.
Can use jumper cables to a different battery that needs charging is one way.
Is there any solar? Various voltages in the low 13s just above battery voltage 12.x, but below converter voltage 13.6 ?