elk lk - camping
since i'm not totally familiar w/ that area, i'm going to "assume" you are talking about the trailhead and parking lot on the road which leads into elk lake lodge? if so, we used that trail to hike into the slides of macomb, which is, i believe the same trail you use to hike into dix. there is both a lean-to and a nice camping spot back in there. not too far in and the hike is flat all the way. i don't think there's any other camping spots in that area. there may be another lean to or something much further in but i don't know. we read the log-in book at the lean-to and a lot of folks stayed there to hike dix and it sounded likea nice place to stay. there's a small creek right next to it.
as far as elk lake "policing" their grounds: i treated myself to a weekend up there awhile back. they own the land to sunrise mountain and clear pond, as well as access to many other trails. i never once saw anyone checking on folks to verify they were authorized on the trails or making a huge effort to police and definitely not to harrass. and, i don't see any reason you couldn't sleep in your car in that one, designated parking lot;since you can leave your car there overnight or for several days. the other parking lot across from clear pond belongs to elk lk and you must have a permit from them to park there. there's a good chance, if a car was there late at night someone would ck to see if it belonged to one of their guests.
but like i said, the lean-to and camping area back in off the state trail are both nice.
hope this helps