Here's an alternate technique. Orient the bike with the rear wheel toward down the stairs, the front wheel toward up. Stand in front of the bike and grab the front rim with one hand, lift the wheel and roll the bike on its rear wheel. You always keep the bike in front of you. For going down the stairs the bike moves backwards as you let the rear wheel drop down one step at a time. For going up the stairs you step up the stairs backwards with the bike moving forward. You keep the bike from tipping by how you hold the front wheel.

This technique keeps the bike in a nearly vertical position which lets you negotiate tight corners easily. It isn't as fast, especially going up the stairs, as picking the bike up by the TT or throwing it over your shoulder and walking. But it is surprisingly easy and maneuverable in tight situations. If your staircase is narrow it will help. But if you have to go three flights it might be too slow going up backwards. Still, it's worth a shot.