Before you purchase filters, I'd recommend checking the power and antenna connections thoroughly.
Start with the power feed. Any connection/joint should be suspect. Any crimped connector should be inspected, make sure it's not loose, corroded, damaged, etc. Work through from the power source all the way to the radio. Check the fuses, too. I've often soldered any connections. Not a lot of solder, but just a touch on any crimped connectors. Marine grade heat shrink tubing can help seal things up too. When in doubt, cut the connectors out and redo them.
Same with the antenna. If possible, try a known/good mag-mount antenna in place of the original. Go through everything from end to end, paying close attention to the connector at the radio and the antenna.
I've seen commercial radios do weird stuff like this. Usually I found a badly corroded antenna connection. Cleaning it up or replacing it fixed the issue. Biggest issue I've seen were NMO base antennas that either were not properly installed, or were so corroded. I had one VHF radio fry the power amplifier section due to a corroded connection.