First, I made a crude setup. It was signal generator connected to an amplifier. It could feed a controlled shape signal limited to +-30V to the gate of the mosfet.

I didn't get any success with this setup at room temperature, to I tried heating up the mosfet. With soldering iron, I heated it ultimately to 400°C. With low negative voltage at gate (-15V), the transistor survived just fine! I am absolutely shocked by how robust the transistor is!

When I cranked the voltage up to the full -30V, after heating the transistor to 300-400 °C, intermittent shorts from gate to source started to appear. They were not destructive (could be recovered by forcing some current into gate, or heating, or both).

The biasing did change a little bit, but it was small, random, and may have even be caused by emergence of slight leaks. I could not come anywhere close to getting a zero or negative gate threshold voltage.

At that point I began losing hope. But I decided to crank gate voltage up even more, but for that I had to build a new setup, because the amplifier couldn't go above 30V.