I've moved all sorts of large, heavy cabs up and down stairs on my own and I've developed an odd method, but it works and puts less strain on the lower back than using a hand truck or the step up/step down method.
Going upstairs, turn the cab so it's narrow side faces the stairs, tip it toward the stairs until it's laying at an angle up the stairway. Grab the bottom of the cab and lift up, the top end of the cab will make purchase on a stair. Push it up end over end until the bottom of the cab, now facing up, grabs another stair or hits the landing. Keep doing this end-over-end until you hit the top of the stairs. This does require some upper body strength, and while it sounds awkward in my description, once you get the hang of it it's quite easy.
Reverse the process going down the stairs, staying underneath the cab, flipping it end over end down the stairs. Again, you need upper body strength or at least some mass to keep it from rolling over you, but you're a big enough guy that it shouldn't be an issue.
Going upstairs, turn the cab so it's narrow side faces the stairs, tip it toward the stairs until it's laying at an angle up the stairway. Grab the bottom of the cab and lift up, the top end of the cab will make purchase on a stair. Push it up end over end until the bottom of the cab, now facing up, grabs another stair or hits the landing. Keep doing this end-over-end until you hit the top of the stairs. This does require some upper body strength, and while it sounds awkward in my description, once you get the hang of it it's quite easy.
Reverse the process going down the stairs, staying underneath the cab, flipping it end over end down the stairs. Again, you need upper body strength or at least some mass to keep it from rolling over you, but you're a big enough guy that it shouldn't be an issue.