You can go cross-country in the SGW – its not encouraged, but folks do it. The most popular XC route I know of (and have done numerous times) is up the northern face of San G from the Dry Lake Trail. Its mostly scree, but you’ll avoid the ‘slog’ a-r-o-u-n-d the peak on the Sky High Trail to the summit.
As for non-designated campsite camping, you’d have to get an ‘explorers’ permit from the ranger station. They usually don’t issue those for popular areas with designated campsites, but will probably give you one if you’re planning to camp on the outskirts or in a more remote area of the SGW.