Not surprised it's not working. L1 or L2 is not supposed to be bounded to ground. In the US, L1 and L2 is 120V vs N (which generally is same potential as G). L1 vs L2 is 240V. In Australia from what I can find, L1 and L2 is 240V vs N.
Note the Tesla UMC when using 240V doesn't even use the neutral at all, so I don't think it cares at all if you have split phase, just that your setup is properly grounded. Have you tried using the UMC on an actual 240V circuit powered by the grid? That would confirm if it's working fine with the 240V setup in your country.
I think your issue is your inverter is either not grounded properly or it was not designed to be grounded in the first place (but rather floating), in which case it's not compatible with EV charging that relies on a ground for protection against electrocution (which is why the later a EVSE you bought doesn't work either).
The UMC works fine when tested with 240v split phase grid power (balanced legs). I know it doesn't need neutral for 240v. With single phase 240v I was able to bypass the ground check by bonding L2 to ground, so the grounding issue is solved. However, since L1 and L2 are out of balance (~90v / ~150v), the UMC can't detect the outlet properly and caps at 8A. It charges fine at 8A.
The solution should be an auto transformer to balance the legs.