Two excellent turntables!
The Sony will be difficult if my experience at attempting to “improve” a PS-X65 is typical. The original oil-filled mat you reference is pretty much unobtainable at this point. Interesting read on their approach:
https://www.vinylengine.com/library/sony/total-system-technology.shtml
The JVC may prove to be more responsive although it appears the original mat was 1.) sized to fit within a recess in the platter 2.) features a slight dish profile suggestive of using a spindle weight or clamp.
With a properly dialed in system, any changes will result is sonic differences so remain objective.