I started reproducing the negative voltage torture with a new mosfet, and it is the same! Well, I didn't measure the actual torture curve. I just found out that it is the same 20-ish volts it takes to observe gate leakage. Either this mosfet is leaky too, or it is just the way it is. Strange.
So I stopped the attempt to reproduce, and will save this LAST mosfet for something more interesting.