Appeared this past warm w.e. that nearly all snow from that last dusting has since melted off on the range’s south and west-facing aspects, with exception of some ice and crust patches on N/NE facing slopes on the higher peaks. [E.g., the Sky High Trail switchbacks on the east side of SG looked to still be iced, well-caked in white as viewed from Lake Peak.] If no storm activity occurs between now and your permit dates you should be snow-less at R.R. Flat.
Be sure to watch the zone weather reports at NOAA National Weather Service (would provide link but this site may block them–see weather dot gov), play the displayed map to zero into the general zone; see also bensweather dot com for daily local obsvs. I’ve no current intel on High Meadows spring–normally considered highly reliable–but South Fork is definitely still gushing aplenty. Deer hunting season runs thru Nov 11, be alert to possible hunter activity in South Fork Trail vicinity.