Having seen that parking for the Pitkin Lake trailhead in Vail is now limited to two days with threat of citation or towing, this is what we did a couple weeks ago when we wanted to do a 4 day backpack on that trail.
Call one of these non-emergency numbers for Vail police: 970-479-2200 or 479-2210 and request "Code Enforcement/Checkpoint Charlie." We spoke to an officer in this division and explained what we wanted to do. The officer took down our car description and license and dates of our trip and gave us the okay to park for the 4 days. Once we parked, we also left a note in the windshield requesting that any officer wanting to cite our vehicle contact the person we talked to in Code Enforcement before doing so. In our case, we talked to a person named "Ryan."
We're not sure if similar limitations exist for the Bighorn parking area or the Gore Creek, but if they do, a similar effort should help.