I would not worry about the road work . You may at most have a 30 min delay going up the road or down! You will be issued a parking permit for the nights you are on the trail when you pick up your Mt Whitney permits that the lone pine Ranger station. There is a temporary parking area at the trail head. Get there early on the day of your hike to guarantee a spot!
I will be up there for my hike up Whitney on the 23rd and will post more info around the 25th.
