There is something very fishy going on here. Why would "stainless" steel rust quickly and then stain? Stainless steel is not rust proof, but that is a bit soon for anything. Were you using pyrodex or black powder? This sort of response to BP seems more like nickel than stainless steel and I do not know of anyone supplying 1851s in stainless, anyway. That does not mean there aren't some out there, but I have not seen them; Remingtons, yes, 1851s, no.
I have left both my blued revolvers and stainless uncleaned for more than a day before a very slight discoloration was observed, and then only on a bare shiny steel place, not on the blued surfaces. Something is not right here.
By the way, I use Ballistol Milk for cleaning my BP guns. It is made of 2 parts Ballistol and 8 parts of distilled water. Shaken well, it makes a very cloudy emulsion; one puts it in a generic spray bottle. It works as a BP solvent; it apparently neutralized BP fouling (which is strongly alkaline), because I can shoot a gun, spray it down, and come back 3 days later to an oily gun with no rust. The distilled water evaporates and leaves behind the oil and BP crud, but with no rust.
All I do to clean is to spray the gun down, wipe, brush, mop and wipe out the bore, wipe down again and spray again. Then I come back in 24 to 36 hours and redo the procedure. After the second go-around, I let the stuff dry to the oily base and store the gun. No rust, ever.