Negative-Gm Oscillator Biasing Conditions
1) M2 needs to be in saturation

The voltage of interest is the common source voltage, not the outputs at \$1.198V\$. Although the cross-coupled pair transistors will act like a kind of switches, they need a certain \$v_{GS}\$ to keep working. This gives us \$v_{DS2} = 1.198V - v_{GS}\$. In order to be in saturation, we require that

\$v_{DS2} &gt; v_{bias,t} - v_{TH} \Rightarrow v_{bias,t} &lt; 1.198V - v_{GS} + v_{TH}\$

So your design for M2 is along the lines of:


\$L_2\$ is big enough to increase its output impedance, and to improve matching for the current mirror
\$\frac{W_2}{L_2}\$ is big enough to drive your bias current (which I assume is a design specification) with a small enough \$v_{GS2}\$.


2) M1 needs to be in the subthreshold region

I don't see anything particularly wrong with your reasoning. However, you might want to consider that:


when the outputs diverge, the voltage that goes down will take the role of the source. \$v_{GS1}\$ increases, and M1 may go out of weak inversion... It kind of depends on the requirements whether or not this is ok.
when you connect the bulk to ground and the source is at a higher voltage, then this results in a higher \$v_{TH}\$ due to the body effect. So you have a little bit more headroom to keep M1 in the subthreshold region.