To repeat, Chiricahua is a very small park, although it is at the north end of the Chiricahua mountains which are quite extensive, with a well developed trail system than affords many multiday trips. However, within the park, the longest trail can be easily done in about half a day. There are no connections with long trails outside the national Monument.

One of the reasons the ranger was doing his evening check of the trail heads was to determine if everyone had gotten out. Note that his call was the correct one.

I would be very leery of leaving a public notice on my car that gave the length of the trip. It is an open invitation to car clouting in too many places. A good many trail heads and parking lots, especially in the western US have no people around, only parked cars most of the time, which encourages breaking and entering.

In many of the larger parks, there are permit systems that tend to track backpackers, although the primary purpose of these systems is to spread use around, and minimize resource damage.