Per Wayne's post of the UL content, the standard does not require measuring the L-N voltage for delta systems. It's always been my understanding that where manufacturers call for a neutral on a single phase L-L inverter setup, the purpose is to distinguish between the 240 and 208V (or other, e.g. 230) grids by measuring the L-N phase angles. This allows the inverter to just start up on either of those grids from defaults, without the installer having to program it. So often the alternative to running a neutral is having to program every inverter all the time. This is basically what the SE manual says as I understand it; if you want the inverter to work with a neutral reference that doesn't show 120/240 or 120/208, then you will need to reprogram the inverter from default. (FWIW I once had a crew member report that a single phase SE inverter worked without a neutral when not reprogrammed from the default. But that may have been a fluky firmware version, I never saw that backed up by a manual and only heard of it once.)
What baffles me a bit is that you originally said the AB inverter(s) were working and only the BC wasn't. And I would have expected neither to work without reprogramming.