Thanks to all at #AmigaZeux for getting AmiNetRadio working on OS4 - it's working very well on my AmigaOne-XE.
The compatibility list does state that the ANRNG GUI doesn't work with OS4, but if I just click 'ignore errors' when the Grim Reaper appears, it does work. The background of the main image is displayed, but the iDot GUI actually looks very nice, and is really clear and simple to use.