A few stove-moving suggestions. First, [pretty obvious] remove all doors, firebricks, grates, handles and inspection covers... You can probably drop the weight by 150-200#. The empty steel box now has lots of 'holes' in it for grabbing hold of the box.
If your turn-around at the top of the stairs is real small, would it help to stand the stove on end?? you may be able to strap it to a good furniture/appliance dolly and move it 'on end' instead of with it's 'feet down'.
Another idea I've used is to make a good strong crate, that has lots of hand-holds. Bolt and screw it together and make it strong.. This was used on an object that just didn't have anything to hold onto.
Keep a strong strap on the stove, and a big strong guy at the end of the strap, and let him control the decent down the stairs... slow and steady will do it. If it gets away from you, lots of damage and possible injuries... don't want that.
I can't remember the design of the feet on the SF models, but member greg white raised his SF150 up about 12-16" and made it much easier to load and empty the ash pans.. Maybe you can remove the legs if needed then weld them back on ?
Anyway, good luck with the move and be carefull...