Trying to make sure I understand what you did:
Using a Form C relay I wired the common contact to the J1772 connector, the normally closed contact to the neutral lug that originally went to the J1772 connector (this is after the relays on the board and GFI CT) and then I wired the normally open contact to the second 120 leg looping it through the GFI CT. The coil I wired from the input neutral lug to the second 120 leg, so if no second 120 leg is present for 240 charging, the common is connected to the normally closed contact which is neutral and the L1 charging happens. If the second 120 leg is present the relay closes and common is now connected to the normally open contact which connects the second 120 leg to the J1772 cable while looping through the CT.
So here, you have 3 wires going through the CT ... the original hot, neutral, and hot2 for 240V. So when you test 240V, only the two hots have current going through the CT, but the neutral has no current going through the CT, because the relay is connected to neutral before the CT. Even though the only current going through the CT is the two hots, which sum to 0, you get a solid red fault?
Then using the output of the relays and bypassing the CT I tried using that route and L1 threw a fault as well as L2.
So when there are no wires at all going through the CT, it throws a fault in L1?
Am I understanding you correctly?