LDCohen
Concerning your GGF, Joseph Sydney Sutton and his service during the ABW, it is my opinion that he would have travelled to South Africa under his own steam and not recruited for service here in OZ. Apart from the official Colonial Australian or Commonwealth contingents seeking recruits, I have never seen any local advertisement looking for men for units raised in SA..
During the heyday of the Old Empire, many unattached men (or even attached ones) travelled widely in search of adventure or fortune. Your GGFs service in the NVAC appears to date from 12/12/99 (some two months after the Boer invasion) and your GGF possibly set out to the Cape from OZ after reading/hearing of events with the intention of seeking placement in a locally raised Corps. Many did so, and by no means all of them have been recorded as doing that. Men have been recorded as travelling from here to SA as "indulgence passengers" (fare paid) and others went as horse handlers. Others just went after missing out in the local recruitment ballots.
Looking at the NVAC nominal roll, it seems your GGF was entitled to one or more date clasps on his QSA medal (notation "KCR"); which means subsequent service in another unit. I had a look on the NVAC medal roll page for your GGF (WO100/ 261 page 64) - clasps Tugela Heights and Relief of Ladysmith - and there is a marginal note to the effect that he also served in the Imperial Hospital Corps and the SALH.
On the IHC roll (WO/100 page 56) I found an "S.Sutton" with service between 3/4/1900 and 12/2/1901 (??? hard to read). However, that appears to be your GGF as the IHC nominal roll on this site shows "Jas. SIdney" as the forenames.
On the SALH roll (WO100/274 page 103), I found "2140 Sydney Sutton" with clasps Cape Colony and Orange Free State. At that point I ran out of time!
I invite you to check those quoted sources and satisfy yourself that they relate to the same man.
I regret that it is really not possible to give you a definite answer as to why and how your GGF got to SA - except to say that it would have been by ship and that a large unrecorded number did just that.
Don't give up hope about finding your GGFs medals. Keep an eye on Dealer's lists and on-line auction sites and you never know.
Best regards
IL.