AM/FM radio interference

We have a low wattage, small car style radio with built in speakers. This is actually the 3rd one we owned like this. One we gave away, the other i fried one day while working in the dark (I don't want to talk about it lol). In general they're great.

Unfortunately, it has an interference problem in that whenever there is a lot of power being put into the batteries, it just turns to static.

So

1 - Is there a filter or something I can hooked into it to stop this?

Or

2 - Anyone have a suggestion for a replacement for it that won't have this problem?

Or

3 - Would I be better off just going to an AC powered radio through the inverter?

To get rid of the static folks would need to get rid of what is causing the static.

Maybe other electrical devices or power lines?

Maybe something to do with the antenna?

https://en.wikipedia.org/wiki/Radio_noise

If you like your present system, I cannot help, but could you be happy with an alternative?  Take the antenna out of the system.  I have several radio apps on my phone....KCRW, WUGA, et al ....... including our local public NPR outlet.  Never an issue with reception or interference,  and the exact same broadcast. Give that method a try, perhaps your problem will be solved.