I suggest this as a quick check of the converter. Measure the voltage at the battery without shore power connected. Next, plug in the shore power and check the battery voltage now. Usually, the measured voltage will be a bit higher, like one volt, with the converter operating and charging the battery. If you have a helper, you can monitor the voltage at the moment shore power is connected, and see the rise as it happens.
As for the radio, I don't know if there is a fuse right at the radio, but it's possible at the back of the radio.
Hate to say this, but transistors can fail faster than a fuse in a reverse voltage situation. Proper circuit design for reverse polarity protection is to use a diode connected backward across the supply, downstream from the fuse, or a diode in series with the 12 volt supply to only allow current in the proper direction. A reverse diode will clamp the reverse voltage extremely fast then blow the fuse in the process. That converter had reverse polarity protection in its design. Your converter may have the protection, and your radio might have as well. Sorry if I'm getting too technical.
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2013 Jayco Eagle 31.5RLDS
2018 Silverado 2500 HD Duramax
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