As Bruce mentioned, Parking is not likely to be a problem.
I highly recommend hiking the first couple miles the day prior (28th), to "scout out" the ledges, and creek crossings. If you do leave early (as indicated) you will be hiking this section in the dark, and there are ample opportunities to get off the trail, and possibly have difficulties with the ledges. Doing this the day prior, in day light, will be of significant value.
Perhaps you know this, but just in case you do not, the Mountaineer's route is not a trail, and can easily be lost.
Good luck, and write a trip report when you get back.