I have the exact same scenario, except I don't have a hand rail to lift over......mine is a wall.
With only 1 friend, I have carried up Stern and Williams games both. Remove the head first and foremost. Then carrying the game body on its side to the landing and setting it down on your foam square or nice heavy rug. At this time the bottom of the game cabinet is facing the steps. One person above the game and one below, tilt the game towards the steps while the lower person squeezes in enough to get it lifted to the first step. Then there should be enough room for the lower person to actually get in there and pick it up. You both carry the game up the stairs, then reassemble at the top.