My kids always seemed to pick the top floor of no-elevator buildings. And those awesome sports teams helping move in the first-year students is a one time thing only. They won’t be there to help you move out, or to move in for subsequent years. I have occasionally used a hand truck but not so much on the stairs. Take your time, it’s okay to need breaks. It sounds like you should be the pile watcher while your child/the help does the actual moving.