Keep in mind that the dimensions of your "box" lengthwise is limited to the spacing of your ceiling joists.
It's fairly simple from that point. If you want your cab to finish out at 36", you've got to cut the END panels at 48" and run up through the sheetrock to attach them to the joists. This is called a "suspended" upper, and you'll also want to run a couple of screws through the cab top into the joists.
The dimensions you specify are going to add up to one heavy box, and it is absolutely crucial that it is well fastened. I suggest that you use 3/4 material for cab "top" and cleat the 48" end panels with 2x4 to the top of the joists. Remember: screws are cheap.
I have hung cabinets as you have described by running threaded rods up through the insides of the corners of the cabinets and fastening from underneath with a fender washer and nut and attaching them to the ceiling beams. This worked out well, as I could pull the cabinets tight to the ceiling.Hope this will be of some help.
Build your cabinets as usual with reenforced corners for the threaded rods and make tubes (same as cabinet) of wood, square, hex, round, whatever to hold the cabinet away from the ceiling whatever distance and hide the rods which should be mounted into heavy supports fastened to ceiling joist in the ceiling. If unable to access attic, use steel "c" brackets inside tubes fastning with lag screws top and bolts to cabinet.
In order for the separator to work correctly, you need to set up a "cyclonic" action inside the can. This means the intake is near the outer edge of the can and a fitting directs the air flow around...