June will be a good time to do it, as you have more daylight. Starting up the Main Trail in the dawn twilight should be as early as you need. The Ebersbacher Ledges are best done with daylight. Make SURE you study the route.
I doubt road construction will be up on the Portal section that early (but I could be wrong). Transportation will be a hassle if you can't drive up and park.
As Steve mentions, with the long days of June, you can easily complete the hike starting in dawn twilight (30 to 60 minutes prior to sunrise). However, I would recommend that you "scout" the route the day before. I suggest climbing up to lower boy scout lake and back as sort of a "warm up" to your hike. Total time is less than 4 hours, and you will know in advance the early part of the hike. As Steve mentions, it can be easy to lose the trail, so this will serve as good orientation (and further adjustment to the altitude).
Hopefully, the road construction will not get in the way of a "practice" day, as well as your hike.
As for your concern down climbing the final 400 or the easy walk off, you always have the option to return via the main trail. In fact, it will give you another perspective on the hike.
John
