I like DGPs setup, that's pretty much what I would envision for a small hydro box. 1 big container with 2-3 small plants in there. I don't know much about LEDs and all that, I just use t5s to veg and 1k HPS for flower and grow bushes so I'm not much help in that department, sorry. I would use a 600 myself and make it a 3 deep x 4 wide x 6 tall space if possible but that's just me. there's too many options honestly, just need to pick something and go with it. get them 10" and flip. scrog as much as possible, there'd be enough room to get some dank flowers. the bins are 16" tall, 10" screen so that's 2' basically. Then you need 12" between hood and canopy, that's 2' left for kolas and 1' left for the hood. done. could kill it in this setup.
If the other bulbs are super cool, you could easily do the size box you are planning and have enough room, I'm sure the LEDs are much cooler than the HPS