Well, IMHO, placing your aeroponic 15" x 15" unit in a space that is 24" x 24", that gives you 4 1/2" on each side of the growing unit, which is ample. Sure envy you having the 10 foot height; you could grow some WHOPPERS!!
Just one more question: How big do you want these plants to get? With four in there, you won't get good light penetration to the bottom of the plants once they take off, but that would mean sacrificing quantity for quality.
I had a thought...you say you have a fem plant already, and you could take clones? Why not start with growing 2 plants full cycle, and see how it plays out? If you see that it could handle a 3rd or 4th, then do it you next grow. But, really, I have to ask again...how big do you want the plants to grow?? Also, do you know the stain?
Nelson