From what I have seen, parking has never been as good (due to the one parking permit per hiking party), and currently delays are only on the lower section of the road, and are not too long.
For your hike, you can always get UP to/from Horseshoe Meadows via Lubken Canyon Rd (about 3 miles S of Lone Pine), and completely skip the road construction.
Coming down from Whitney Portal, the "extended delays" period is from 1 PM to 4 PM, so your shuttle will get through after 4 PM.
