One possible solution. Get a PVR / DVR instead of a set top box to receive TV. That will have an antenna input and output. The output is designed to provide a signal to a TV but you could use it to plug into an FM radio and it might let through the FM frequencies as well. So you wouldn’t have to get the splitter.
However, note that the DTV antenna designed to receive TV from Melbourne (channel 6-12) isn’t designed to pick up FM radio which is on the old TV channels 3-5.