Is this something like a glass plant where a shutdown is devastating? That is usually where you see floating delta.
I am not sure how you will isolate this but I do think you have leakage in one of the loads, pretty close to one end.
It might be interesting to ground the 486v phase through a fairly high value resistor, 100k ohms or so, and see what it does to your readings. If you significantly change the readings you have a high resistance fault. That would just be a calculator exercise to figure it what the resistance of the fault was.
A very high resistance fault might be able to give you this symptom without really being a problem if you had another bolted fault but if this is the first bolted fault inside a heating element or motor (no significant change with the 100k ground), you would certainly know which one it was if you had a phase to ground fault. It would be the one smoking. Hopefully the breaker would trip.