The Dashboard and Radio are most likely on the same CAN bus, so there isn't anything you can do to stop it. If they were on different CAN busses, you might have had a chance by doing some quirky stuff to the car's gateway (hacking, reflashing, etc, but that is hard hard work) so the message does not get routed to its destination.
If I read you query correctly, as an option, what you might want to do, (but this means tapping your own CAN transceiver onto the bus) is send your info to the dashboard. When the message comes from the radio, detect it with your uC and send your info message again, a few milliseconds after the radio status message was sent. That might just force the dashboard into displaying a continuous image.
I can't really think of any other way to do this right now, but if I do, I'll leave another reply.