Amazing Grace....what state do you live in? where do you leave your 'Sig on your side' when you are entering buildings and/or place that don't allow CCW? like state/federal buildings, college campuses, any building that has a sign that states(with picture here in my state) 'No CCW', bars, arenas, etc. etc.
If it's not stated in your states laws that you 'can't' have a loaded weapon unattended in vehicle i don't see the problem. Here in Arkansas, without a CCW you can carry a 'unloaded' firearm, the ammo/magazine just must be kept seperate from firearm. With a CCW you can have a loaded weapon to conceal carry or unattended in parked, locked, vehicle.
I don't understand what you mean by amount of paperwork involved. You call the police, they fill out a report. It would be no different than having firearms stolen from your home. Unless the firearm you mentioned was unregistered? Or not registered in your
name? And on the plus side, reporting firearms stolen releases you from liabilities if used in a crime or someone is injured by weapon.