Good question, but I have no good answer. I have not done enough modelling to assess the relative importance of the various current surges at startup and shutdown. Then time constant of the output tube's cathode emission is also unknown quantitatively, as it depends on the thermal mass and radiation efficiency of the filament as well as its temperature/emission relationship. Tube makers are a little secretive about some of these variables...
Still, I suspect the fastest transition and hence peak magnetizing current is charging the parafeed capacitor through the plate choke. That would happen before any of the cathodes start to conduct. Interesting to speculate - it's conceivable that a relay coil in the cathode bias circuit, shorting the OPT primary until the cathode draws enough current to actuate the relay, would do a good part of the job.
