I have absolutely no problem syncing my PSOne to any screen.
Try fiddling with “Analog sync LPF”, “Analog sync Vth” and “Vsync threshold”, I am sure you will find a setting that syncs.
Usually lowering analog sync vth to 56-67mV works for me with troublesome consoles or ‘sync-on-luma’ cables.
I did notice that having shared ground (through video cables) to the OSSC and my CRT, resulting in lower quality (noisier) sync signal and the default vth of 123mV loses sync.
Unplugging the CRT from the main power and suddenly the Console+OSSC syncs with vth 123mV.
Again, some sync problems are from noisy power supply or interconnected equipment.
Try disconnecting all other devices from the OSSC (including HDMI) and leave only the console and OSSC.
Did you try to change your PSOne power supply?