First off, the inverter and converter are two totally separate animals. The inverter turns 12 volts into 120 and the converter turns 120 into 12. You mentioned the inverter turning on and off. Typically those things remain on and don't cycle. You just turn it on and the 120 volt device receives power.
The converter will cycle through different output levels but does not cycle on and off.
By feedback, are you getting a high pitched squeal in the radio or a lot of hum? Is the feedback only when the radio is in use of is the noise the same with CD and DVDs? If only on radio the interference could be coming through the air. If the problem is there on all functions, it probably is coming through the power line.
Both the inverter and converter should be well filtered devices to prevent "noise" from getting into the power line or be emitted through the air. That being said, the most obvious thing to try is replace the offending device. But you have to narrow it down to either the inverter or converter.
Sure you could try adding a filter to the power line but that may not completely help.
__________________
Jim
Retired electronic technician (45 years in the field)
2017 Greyhawk 29W (solar & many other mods)
wife (maybe I should have given her top billing)
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