1) In the market that I am familiar, PTs for such applications are specified as 277/120 V with a 1.8 over voltage factor.Client/consultant will also insist to energise units at 1.8 E for some hours during testing at factory. Scottf may correct me if my understanding is not correct. Such PTs are designed with a B of 0.8 T against 1.6 T, normally used. But even with such specifications also, neutral inversion can occur in PTs in ungrounded power system.
2) I faced such a problem nearly 30 years back. We were handing over a newly installed 315 MVA 400/220/33 kV transformer bank with tertiary formation by aluminum bus. There were 3 numbers 33 kV PTs with 1.8 overvoltage factor connected for ground fault protection on tertiary side. A broken delta(we here, call them open delta) secondary of 110/3 V was provided for detecting grounding. When bank was commissioned, 20-40V appeared occasionally across the broken delta and customer refused to take over the bank claiming some defect, some where. It took me couple of months to resolve it. I had no idea of this phenomena and with much difficulty I could collect the relevant papers (remember there was no internet or google)as attached. After studying all the literature, I came to conclusion that to solve this neutral inversion, there were three solutions- add a resistor across the broken delta, load the star connected secondary of PT with star connected resistors or add shunt capacitors across the primary 33 kV bus. Client was any way planning 33 kV Surge absorbers at tertiary terminals to mitigate the transferred surges. When these were put in to circuit, problem disappeared.
3) The reason for this is due to mismatching of magnetizing reactance of PT with zero sequence capacitance of the primary bus. In an ungrounded circuit of iron cored reactance with capacitance, oscillations can set in for a range of C and X, fed by a sinusoidal voltage.So this problem is more where the bus is short ie capacitance is less. With long lines this will not be there due to higher capacitance offered. The resistor will create equivalent voltage drop in primary so as to shift the inductive and capacitive branches going in to oscillations. Please see the 1931 paper by Boyajian (From GE, Pittsfield) for more details.