be designed with ultra-high $Q_o$. This is achieved by increasing the thickness of the devices, thus increasing $n_{eff}$ and lowering the air-mode band-edge frequency away from the light-line. Motivated by high $Q_o$ optomechanical SBC’s and PNC’s [@Hryciw:13; @Healey:15], we then design devices based on elliptical holes that mode-match to a physical gap introduced within the PCC. Due to the higher optical bandedge frequencies of these devices, the standard deterministic design approach fails to predict the highest $Q_o$ device. However, by substituting a highly elliptical hole for the centre hole and tapering to circular holes we can lower the band frequencies and achieve an order of magnitude higher $Q_o$ than predicted with the deterministic procedure. We then further extend this highly elliptical hole design to add mechanical degrees of freedom and create high-$Q_o$ SBC and PNC designs. These devices combine the excellent mechanical attributes of Si$_{3}$N$_{4}$ with the sensitive cavity-optomechanical transduction of earlier Si based designs [@Kaviani:15]. This is predicted to allow their room-temperature thermal motion to be detected in a nonlinear optomechanical measurement whose power spectral density (PSD) is observable above system noise levels. We also show that in cryogenic conditions, observations of thermally-driven nonlinear optomechanical phononic Fock state quantum 