I managed to complete the rosette this morning. There's no hint of chipping which has frustrated me in the past, thanks to a tip I picked up from a long-forgotten source.
Prior to routing the inner and outer purfling channels that border the rosette, which I complete after the inner tiles have been glued in place, I applied Titebond to the soundboard in the immediate vicinity of the rings and let it dry overnight. The rationale for doing so is that the wood fibres of the soundboard are less likely to tear or chip when the channels are routed as they are supported and stabilised by the glue. I believe the original suggestion involved the application of shellac in the vicinity of the rosette, but as I'd already managed to smear some Titebond on the soundboard when gluing the inner tiles, I figured it would achieve the same goal. Mission accomplished!