One common problem with corner gounded delta systems now is the increased use of electronic power systems, specifically the protection systems often built in to them. For example VFDs; 9 out of 10 VFDs are now made overseas. In places OTHER than the US and Canada, they NEVER see delta power systems, let alone grounded delta systems. So they use surge protection devices on the front-end of the VFDs to protect the diodes that are designed ONLY to be used on grounded Wye systems, i.e. 480/277V. The problem is, they use a gounded Wye connection of the capacitors on these surge protectors, and if you connect a grounded Wye system like that to a grounded Delta source, the reference voltage to ground on two of the caps jumps to line potential instead of Wye potential, i.e. the voltage that 2 of the caps see is now 480V instead of 277V and one sees zero volts. This has a tendency to pop the 2 caps in short order (because they would NEVER think to use caps rated for the higher voltage just in case, it would cost 23 cents more each). Then if one or more shorts instead of opening, you get all kinds of fun stuff happening.
So take a look around, this can be the case for VFDs, UPS systems, large 3 phase power supplies of any kind, some smaller computer or PLC power supplies, even some general machinery that has been imported from overseas where some smart ass engineer thought he might put in a surge arrestor just in case his machine ends up in Dumbunnystan somewhere where voltage is an on-again / off-again affair.
USUALLY they will have an instruction sheet that tells you something like
"WARNING! REMOVE THE SURGE PROTECTION IF USED ON A GROUNDED DELTA SYSTEM"... but nobody reads that stuff.
The quick way to start on this is to disconnect ALL of the loads on the transformer and measure again. Measure phase to phase, then phase to ground. If you still have the anomaly, you probably have a bad ground connection on the grounded phase, or a bad transformer. If the problem goes away when the load is disconnected, someone connected a formerly useful device to your system without reading the manual (or understanding what the impications were).