You are right with the frame and there are reasonably cheap lasers, then it becomes exact.
It is also correct with threaded rod, take 6 mm then (I don't know if there are thinner ones), that will do fine.
Then it can be adjusted exactly by the mm, the attachment in the ceiling, maybe the plumber's Z-iron with washers can be a good mount in the ceiling and with some string to follow for the mounts.
It will probably work, and the nail will be straight
