When the 3V3 side of the Fet is pulled low, it first pulls the 1V8 side low through the body diode of the FET. which explains why it goes to only 600mV.
According to the datasheet, the threshold voltage of your Fet is between 450mV and 1V, so there should be enough gate voltage to open the fet and let Rdson "short" the body diode so the source goes lower again, but apparently that does not happen. So start with measuring what the actual gate to source voltage is when the 3V3 side is pulled low.
I recommend to also put a fet on a breadboard or something and measure the actual threshold voltage when it turns on.
Also, you should study the circuit further so yo fully understand how it (should) work. It's a quite clever trick from some Philips application note from 20 or so years ago.
But also (again). margins and tolerances become more difficult to manage with such low voltages. It may be better to use a dedicate level translation IC for this low voltage bus. Or open the trick bag. Raise the gate a bit above the 1V8 level to shift the threshold when the Fet switches a little bit.