Jdog,
I was picking the brain of someone who has some relevant prior experience in park policy and their opinion was that spending some effort in establishing an email/text notification system would be very beneficial in proactively alerting folks of closures *before* they arrive rather than after they've already made the trip. The main driver is there is to alert them of the closure before they get geared up and make the long drive because, without such, in many cases, they may decide to just ride/hike anyways since they're already there. Trail head signage is realistically too late to be truly effective for the general public and you can ostensibly avoid a lot of angry park goers in this manner.
If the park is part of D&R, you can broach the subject with the park superintendent of adding a notification under the existing state GovDelivery system in the same fashion that Island Beach SP was done (for closures, parking status, etc). Apparently its fairly trivial since the system is in place and resources are easily added without much beauacracy. The super can escalate it up and it will get handled without her needing to manage it. 6M gets so much traffic for its density its a prime candidate.
From there, going back to the on-site signage issue, it would be really beneficial to compile a list of resources to add to the signage to inform the public of how to get added to the list, method of notification delivery, frequency of notification and any other resources they can check on the fly for current, up to date status (trailforks, MTBNJ.com, etc) and lastly alternatives in case of closure. Again, using IBSP as a benchmark here.