There's not a single trolley in existence that would make it easier to move into place. It is however very easy to move, we have granite tiles, so we just put a blanket under it, and it then slides very easy, that's also how we moved the uniTower into place.
The problem is one of physical dimensions, its 2010mm tall, which is taller than the door opening, so has to be tipped over at angle, then stood up once through.
The width is exactly 600mm, which will fit through the doorway, but then you have to rotate it through 90 degrees to get it into the gap, which wasn't an issue before, but is now.
If you rotate it before moving it through the door, then it is wider than the opening, depth front to back is about 672mm and the maximum width of the door opening is 668mm, hence I took the doors off, which means it will fit through when turned the correct way to slide back into the gap.
It may turn if I took the washing machine out, as that sticks out about 50mm more than the worktop.