An example for point 4 above:
If we set MaxStep larger than your final Vbias, TCAD selects its own bias-ramp-up strategy (it still doesn't go from 0 to vbias in one solve). No problem. Let's call it "auto ramp-up". Sometimes it works, other times we select a ramp-up strategy using small values for InitStep, MaxStep, and so on, and then it works. Call it manual ramp-up.
But get a load of this. When it works for auto, and we still decide to do another run with manual ramp-up, with each step equal or smaller than the smallest step from the auto ramp-up, it still fails sometimes (fails to reach final vbias), even though we didn't change the mesh, didn't change the physical models, didn't change anything else about the system! Another way to put it: if we're failing at manual ramp-up no matter how small of a MaxStep we pick, what might work is to not do manual ramp-up at all, but instead set MaxStep larger than final Vbias and not specify any value for InitStep and MinStep.
Point being: if larger steps work, smaller steps should always work (it should be impossible to fail in a run with smaller steps). But that's not the case observed here. TCAD is quite a beauty isn't she?