Yes, a run-to-waste sog setup
The tray/s would only need to be about 6" off the ground, basically just high enough to accommodate drain fitting and an elbow. This is assuming you can pipe the drainage out of the growroom this way.
Couple that with the DE setup i'm talking about, it's doable. I do it at one of my setups
16 plants per 4'x4' tray. A basket drip stake per plant(2 is safer though). I prefer 1 gal mesh bottom pots with coco. But have done it with other media many times.
If you can mount the hood(without ballast, or that nanolux) directly to eye bolts in the ceiling: between the fixture and the 3' space needed, that's a little less than 4'. Leaves you a little more than 4' for tray and plants