Can the Sirius radio be set to a different FM frequency?
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If your Sirius Radio has an audio output and your car radio a cassette
player ; you will be able to either homebrew or purchase an audio cassette
shaped transducer with an audio input ,which you stick into the cassette
player , such that by "playing the transducer" you can listen to its audio
input being the audio output of the Sirius radio.

That would solve your 'free FM channel " problem , although perhaps with a
somewhat reduced sound fidelity compared with the FM radio route.

A long time ago I have seen articles for homebrewing the above transducer.
It is a coil inside the cassette placed at short distance from the cassette
players 'head' ,the coil being fed by the audio signal source. It is also a
simple way to connect a ham radio transceiver to the car's loudspeaker
system.
I thought that Ratshack might sell the above type of transducer.

Frank GM0CSZ / KN6WH