Hi.
To get oscillation run for long time the transient analysis, and use TRAP integration method instead of GEAR,GEAR2 or else.
For faster start-up you can help with addition of transient noise in Spectre (if you use Cadence), set initial condition for the L or C, or couple a voltage spike to M1 or M2 gate.
I cannot recommend you other architecture, I don't know this circuit either so I don't know what is the function of R1,Rp. I guess they are loss model of inductors. This figure seems is coming from Razavi's book, there should be explained everything you need.
I recommend you to check loop gain of the connected amplifiers, separately is not the best.