i'd bet the complaints are coming from the canal side. The field, Iron, and concrete bridge areas.
Easy to park and assess, and some of the most sensitive places. The park people are not walking the twisties, or 27side red.
Closing the canal and jaques trailheads, and putting a red light at the middlebush crossing might be the biggest gain for smallest work.
Easiest to do with digital signage, even appropriate daily messages like "MTBikers must be off trails by 8:30am"
might make a difference. A couple people, and some smart weather data scraping might help automate the process.
can't close the lots - the hunters, and others should have the access they deserve.
Now, what is the penalty for trail damage? not mountain biking specific, and how to enforce it? Window fliers on cars with bike racks
announcing future enforcement actions? Taking plate numbers, and looking for repeat offenders? (might not work, people road ride out of the lots too)
Are the park rangers the same as park police? I doubt the rangers i've met want to be that adversarial to the point of giving out tickets,
but they would be willing to explain the damage being done.
It is such a popular park, you'd think that $$ for a pilot program would be available.
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And yes, people go right by those signs at Nox, but do they do it when it is muddy?