[old_tv_nut]

A couple of comments:

Phase shift at low frequencies could occur if your scope is set to AC coupling. If you have been using AC, switch to DC to double-check.

The 100 microfarad source capacitor is a 27 ohm impedance. It's no wonder you have too much gain, and the circuit is non-linear. I'd suggest bridging the 330k, removing the 100 microfarad, and changing the source resistor from 4.7k to about 2.7k. This may require adjusting your gate bias, which I have not calculated.
This will reduce the gain dependence on the FET transconductance and linearize the circuit. Of course, eliminating the 330k will mean more loading on the preceding tube circuit, so the gain there may be reduced, requiring some increase of your FET amplifier gain. I have not gone back to the original circuit to calculate the loading of your amplifier compared to the original circuit loading.