Use Flitz polish, it will not harm the bluing. You may want to pick up some slp2000 EWL and use to keep the metal protected. I use it to clean the bore and the benefit is that it will make cleaning the bore a lot easier. My shotguns do not ever have a buildup of wad residue. Running a bore patch results in the plastic residue coming out in one sheet. You may pick up some silica bead dessicants to hang in your safe. They are reusable. When the dot on the side turns pink, put them on low heat in the oven for a few hours and they are ready to be reused. They are relatively cheap and moveable.
Get a golden rod dehumidifier for you safe.
Wax or put oil on you gun when putting them away and do not touch the metal with your hands. I use rubber gloves and have no problem over 40 years.
Try some Break free CLP to remover the rust. WD40 will also work.
What is the ideal % humidity to store firearms? While reading this post I glanced at the humidity reading on my gun storage area and saw that it was 57%. It usaually is between 50 and 55% and have never had any problems with corrosion.
Heating the air inside your gunsafe does not reduce the amount of water vapor in the air, it raises the temperature of the air enabling it to hold MORE water vapor. But, if more water vapor is not available, it reduces the relative humidity. Use a dessicant , two if necessary. A digital humidistat is available at WalMart, HD etc. for $10.
50% humidity at 70 degrees is considered ideal "Arms Museum" storage conditions.
Any dryer that that and you will have problems with wood stock drying out nad shrinking/checking.
Rust is unlikely to form below 65% humidity unless salt is present.
I try to keep my gun room at 70 degrees but have noticed that the humidity levels vary from 50-55%.
I have my gun room in the basement garage. The other day my wife mentiond that she had seen mold in the garage (this year has been a very wet rainy one), my reply was "it's no big deal". A couple of weeks later I went to my gun room to find that everything was covered in a light moldy film, even inside the cabinets. The inside of my two safes were perfectly fine, I have one Goldenrod in each.