600bar - forget about SMD!
+-0.05% FS psi is quite demanding for that temperature & pressure range.
You are probably aware of Quartzdyne who market calibrated sensors for your application, +-0.02% FS and ~5-20KUSD.
They will likely be unavailable to you at the moment, assuming your country flag is set correctly.
There are very few other (none?) viable resonating pressure sensors openly available for your temperature range.
So, pick a strain gauge, do your own calibration (you have a dead-weight pressure generator, right?) and you may get to +-0.05% FS.
Kulite, Kistler, Keller, Paine, Sensonetics....again, availability in your country may be an issue with some of those.