Sorry to hear your having troubles with the Browning. I've removed rust on fine guns with #0000 steel wool and a good quality oil such as 3-in-1 or the like. Make sure you use the oil liberally or the dry steel wool contacting thesteel may have a detrimental effect the bluing. It will remove the rust though and if it was bad enough to cause pitting, it will now show. If you're going to store them long term RIG (rust inhibitive grease) may be the best option. It'll have to be applied thick covering the surface.
If you're going to be handling them from time to time, or checking on it periodically (monthly) you may want to use something with less mess. I use Birchwood-Casey"Sheath" products ( now marketed as "Barricade"), you can buy the 10 oz. spray can or the "industrial" strength stuff.
Good luck and welcome to the forum.
Here's a fewlinks with info...
http://www.birchwoodcasey.com/sport/...amp;prodcat=75
http://www.birchwoodcasey.com/rust/index.html
http://www.midwayusa.com/eproductpag...eitemid=496433
http://www.6mmbr.com/corrosiontest.html