I was there this past weekend (Fri-Sun). Road to the hikers trailhead was in good condition. The Symmes Creek crossings (4) at the beginning were not a problem but the water volume is high (above ankle) and the flow strong. Suggest taking Tevas's for the crossings so you don't get your boots wet.
The large winter avalanche in Symmes Canyon is still very visible. The FS did a good job of clearing the debris on the trail. Trail to the saddle over to Shepherd Canyon was in excellent condition. We did not encounter any snow until Anvil Camp. Trail after Anvil was spotty due to larger snow patches but once found it was good to just below the pass. Shepherd Pass still has a large steep snow slope covering the trail. Early morning crampons and ice axe needed.
Pass was virtually snow free just a couple of large patches. Williamson Basin however still has an abundant amount of snow as you hike over to Williamson. The W Chute had snow where again ice axe and crampons are needed. Tyndall had a little snow on the North Rib.
Overall, I was expecting a lot more snow having seen how much was around Onion Valley the month before. Snow will not be a problem for you since in a weeks time there will be even less.
Have a nice trip.