It seems "not yet". The *focus* of the architect menu is reset when you switch between floors (a by-design game feature which has not yet been overcome).

I'd recommend making a stockpile and having the furniture moved to the stockpile on the floor where you'll be installing it.

Ah yeah totally. I figured out this too, its really the only way. Have a small furniture stockpile set to bottom priority on each level by the stairs somewhere. When you want to reinstall something from floor to floor, uninstall it, set the priority of the furniture stockpile of the floor you want it moved to very high. Eventually it works its way there then you can install it. Appreciate the comment!