If you keep moving them they can't attack though... maybe use this trigger so they can't click on the unit:
[center]
players: (players you want this to effect)
Conditions: Always
actions: disable doodad state for (unit) at (big location over map)
enable doodad state for (unit) at (big location over map)
disable doodad state for (unit) at (big location over map)
emable doodad state for (unit) at (big location over map)
disable doodad state for (unit) at (big location over map)
enable doodad state for (unit) at (big location over map)
Preserve trigger.
[/center]
but do that like a hyper trig.
I hope that'll help

EDIT: Forgot to say that I didn't know lifted buildint work either
