For longer-term (guarantee 2 years, but I find it lasts longer in Ohio climate), I've been using a pump spray bottle of
LPS-3 for the last ten years or so.
LPS-2 also has a corrosion inhibitor and looks and smells like the original Birchwood Casey Sheath product, which I expect was supplied by LPS on an OEM basis. It seems to me that 1 year was the number they claim for this thinner product.
If you have a lot of rust, get some Gunzilla bore cleaner. Apply it to the rust and wait 24 hours and then use a little more with your steel wool to get the rust off. When I first saw this product at Camp Perry about fifteen years ago, the maker had a sectioned shotgun barrel that was badly rusted and pitted and to which he'd applied the product to one half and did as I described and the rust was gone.
I once let some Gunzilla sit, forgotten, for about six weeks in a '03 Springfield barrel that had some rust pitting. When I dry patched it out, all the rust color came out and my Hawkeye borescope showed nothing but clean, shiny steel left behind. The pits had been glazed with carbon, too, and all that came out with it. There were separate black and rust red places on the patch. Not a trace left behind and no elbow grease involved. I subsequently took a rusted piece of steel and submerged it in Gunzilla and watched over a period of about three weeks as the rust fell off and accumulated in the bottom of the vial I put them in. Pretty amazing. The owner said his chemist told him it breaks the rust and carbon bonds. It needs a little time to work, but does great when it gets that.
If you go the gun safe (or just use a cabinet with a door), you can save yourself the bother of reconditioning a desiccant by using a GoldenRod safe heater or another low-power heat source. They work by raising the temperature of the air inside a few degrees. That increases the ability of the air to hold dissolved water, which lowers the relative humidity. It's the relative humidity (relative to the dew point) that matters and not the absolute humidity (total mass of dissolved water in the air) that matters to rust. The warmed air effectively holds onto water better which keeps it from creating mischief like causing rust.