The first part in the Cape seems a bit leisurely, for example you've allocated a whole day in each direction to driving between Cape Town and the winelands/Hermanus, which are only 1.5 hour drives, wineland to Hermanus is an hour. Depending on your interests you may not need all of the full days in between.

Have you thought of doing Lions Sands first? We did this last year and there is 1 daily non-stop flight from Cape Town to Skukuza which is actually within the Lion Sands reserve. It's more time efficient than connecting in JNB and means you easily make the afternoon game drive on that day. You can fly back from Singita to JNB when you leave.

I'd second considering only 3+3, you're already moving around a lot on the trip

Have you thought of adding Victoria Falls?

Just as a frame of comparison we did Cape Town + Hermanus + Winelands + Lion Sands + Victoria Falls in a week with some careful and efficient planning, although it was a little on the regimented side!