A ranger at Mammoth Lakes Welcome Center?told me to use the road-side parkings along Mammoth road before Mammoth Mountain Lodge for a long-term parking when I did a Sierra High Route from Italy pass to Mammoth in 2019.
You can check/confirm this with a ranger when you pick up you permit (by email)??
BTW, we used?Mammoth All Weather Shuttle (MAWS) () for a shuttle from Mammoth to Italy Pass trailhead.
Ken Toyama