Well first off you are going to wish you had more height. 42w cfl's are pretty big! Even if you hard mounted it you would be maybe 4" off your ceiling. they do get sorta hot so fme, not running an internal fan in my box, I can only get about 3" away. You can get by with a 4" tall pot, so at most you can run about 9" over your dirt. Probably doable but stick to indicas that don't stretch much. Even LST'd plants stretch in flower. My current gear starts out a couple inches over the pot tied down all pretty like and jumps 10-12 inches before the stretch is over. It is a sativa leaning hybrid, but not a super stretchy one. I wouldn't mess around with hanging your fixtures, just put blocks under your pots to raise them up... hanging fixtures take up space and you want those bulbs at the top of the box. A better solution for this would be pl-l lamps. They are easy to wire and not overly costly. You could do 4 of those across the top and be rockin 210w of HO floro at about 1" from the top of your cab. 4 @ 55w, 22" PL-L's and a ballast would run you about $80-100 including the connectors.
The way you have your filter outside the box may or may not work. Most carbon filters are designed to have air pulled through them so they are placed in the cabinet. This would be the biggest need for more height in this design. Most fans operate most efficiently that way (pulling through). Depending on the design you are planning on using, the way you have it now may or may not work. If you haven't researched that you should. There are diy plans out there for a small carbon scrubber that uses 2 mesh pencil cups you buy at walmart, and that would probably be a good size for this box.
Looks like you are wavering between hydro and soil. Is this your first grow? FME, custom mixed organic soil is the most newbie friendly. There are many recipes out there that just require water all the way through until harvest. A good organic mix will also lessen the chance of you having any PH problems. PH problems are a pita because they often show as deficiencies and it is hard to know what the girls need. Also common for newbs is over feeding/nute burn and that is also eliviated by using a "set it and forget it" organic mix. You don't even have to flush organics like you do typical fert schedules. You can spend tons of cash on organic ferts but there are simple recipies out there that only require a couple bags of inexpensive dirt and only dolemite lime, blood meal, and bone meal as additives. I found the organic thing very forgiving and much easier than fertilizing in your water.
I didn't really see anything about light sealing. I assume you know that you MUST have perfect darkness during lights off when you are flowering.
Thats all I can think of. Looks like a good start! It looks like a box that could grow buds!