I worked as rigger for a while & routinely moved heavy machinery, CNC machines, printing presses, clean room equipment. One of the most versatile tools we used was a set of Rol-A-Lifts that can be rented from a lot of places for less than $100 a day & two guys can easily maneuver a safe around with them.
https://rolalift.com/
We had motorized stair climber dollies that I used to set movie projectors upstairs in theaters that would be perfect for safe moving where stairs are involved & I'm sure the pros use them. There's no need to risk hurting yourself or damaging your home with the tools that are available out there, there's a time to be thrifty & a time to spend wisely.