Given this is the only guitar with a problem, after a new battery I would inspect the Matrix UST.
Since the Matrix is installed from the top, it is wired with screw connectors to the preamp or uses a miniature plug. I would check that connection for a loose screw or oxidized plug (pull the plug and reseat it).
If that is all good, then gently move the wire from the UST in the guitar and see if that stops the hum or makes it worse. The solder joint at the UST is fragile and can crack.
Finally, I would gently lift the UST out of the saddle slot and check for a ripped shield.
The Matrix sounds better than a coax UST but its shield and solder connection are fragile.
Replacements are plentiful on-line and you might find a very cheap gray market or counterfeit good enough if a US vendor's real thing is out of your budget. There are not that many options in making a UST and the cheap stuff is likely the same piezo polymer.
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