You can pick up a reserved permit at any permit station--provided that their computers and phone system are working. (This was an issue last year in Tuolumne.) Note that most of the wilderness permit stations close fairly early in the afternoon--3 or 4pm. I think getting to the BOF office by this time based on an 11:45am landing is going to be a challenge.
My recommendation? Try to reserve a permit for the following day, and spend the first night in the Tuolumne backpacker's camground (which your *reservation* will allow you to do) for peace-of-mind and to get some high-elevation exposure before the hiking begins. Since you probably won't be able to reserve Cathedral (or Sunrise, Young Lakes, or Lyell Canyon) for the 17th, you may have to reserve a less-popular trailhead to start your loop, which may mean leaving out a camp or two.
One suggestion (if I got the dates right...): Mono Pass T/H, night of 17th at Alger (or Gem) Lake, 18th in upper Lyell Canyon, 19th at Vogelsang, then continue the HSC loop in either direction.
Another: Murphy Creek T/H, 17th at McGee (or Glen Aulin if the ranger says it's OK--seems to depend on who/how nicely you ask...), 18th in Lyell Canyon near the Ireland Lake jct, 19th at Vogelsang, then onward to Merced/Sunrise/May.
A third (more advanced): Nelson Lake T/H, 17th at Nelson (well-marked cross-country, but steep past Elizabeth Lake), 18th (via Reymann Lake--also cross country...) and 19th at Vogelsang (excellent day hikes in this area), then onward to Merced/Sunrise/May...
A fourth (even more advanced): Budd Creek T/H -> 17th at Matthes Lake (cross country past Budd); 18th at Reymann Lake; 19th at Vogelsang, onward...