Phase noise reduction in LC oscillator with a high-loss capacitor
XY problem, you have what is effectively a capacitor microphone element, with one side grounded and you wish to build an RF Mic. 

Were it me, I would not make it part of the oscillator instead using a crystal osc, and putting the transducer in a bridge circuit. Use a couple of fixed inductors and a piston trimmer or such (shunt it with a variable capacitance diode so you can servo the operating point to compensate temperature drift), then do phase detection on the bridge output voltage.

A couple of inductors, a piston trimmer, a varicap diode, a crystal osc, and some sort of phase detector (maybe a diode ring mixer?) followed by a lowpass filter and some opamp bullshit, job done.