I have had a look at the "Road Route Numbers" dataset myself and it appears to just be R1; whereas South Road between Richmond Road and James Congdon Drive, for example, is designated R1 and A2 (I struggle to think of another such case). The corresponding signs also state both.

Interestingly, I noticed that they've got Victoria Road (to Outer Harbor) designated A16 in that dataset, despite the corresponding signs stating A9.

That stretch of Greenhill Road is most definitely R1 (as stated by the signs on approach to both intersections - unless they're incorrect!)

It's possible that was the case in the days of the old A21 ring route, of which Goodwood Road between Greenhill Road and West Terrace was a part.