I suspect there's something you're missing in the procedure, Rabbit. Snapping in MOI is just as quick and easy as it is in sketchup and Rhino.

1) Select the bottom floor.
2) Click the "Move" button under the "Transform" tab.
3) Click on a point on the bottom floor.
4) Click on a point on your reference geometry, but keep the mouse button pressed in so you can drag out a construction line in any direction. Let go of the mouse button once you have the construction line oriented the way you want.
5) Click on the desired location on the construction line to complete the move.

My apologies if you already understood this - I just kinda got the impression that you didn't, and Michael's answer didn't address this possibility.

Oooh, Michael's next reply has animated pictures! Showoff.