2N7000 behaviour explanation
One thing you haven't considered is that the particular 2N7000 sample you're experimenting with may be faulty (you could easily damage it with an ESD for example). Or perhaps you have got an STP55NE06 with a far better gate insulation than the spec requires, and an 2N7000 which just barely meets the spec.

I suggest you repeat your experiments with a different 2N7000 sample. Chances are the weird behavior will go away.