The bottom, if cut square should help hold it square. The other factor would be how square the edges are of the pieces you're assembling. Since it was cut on a CNC, are the edges cut exactly 90 to the surface? If not, getting and holding it square during glue up will be challenging.
So I suggest you use some 90 degree L shaped blocks clamped into the corners to hold it square. I personally would cut an exact size, square piece of ply or mdf that fits the inside dimension, to brace the framework on the bottom of the structure to set that square. If the bottom is solid already, that will hold the framework square on the bottom and you'll only need the L brackets to hold the top. You will only be able so do a little adjusting for any racking since the MDF cannot be torqued the way you can with real word. Twist it much and it will fail.
If you drop this MDF structure, it will likely fail. You could reinforce it with some light weight aluminum L shaped extrusions. I would have made it from solid wood (like interlocking face frames) or ply.
I made a simple box fan filter many years ago and used a commercial filter holder like the one in homes. The casing is ply, assembled with pocket holes. The filter holder holds everything square. I took the box fan apart and installed it in the box. The other side had a simple vent cover. I installed the 3 position switch on the bottom so I could reach it to turn it on. The box fan never had the power to move much air. It would have required a much higher hp fan to be effective, something you might consider purchasing, perhaps a used commercial unit.
Four filters of any quality is going to cost $40-$50 a set to replace. I found a WEN hanging filter on sale for $99 at WalMart online, picked it up at the local store. It has a remote, plus 3 power levels, and a timed shut off. Works far better and is more convenient to use than my home made gadget. When you hang any filter of this type, install it near a wall so you get circulation going in the shop.
I spent a lot of money trying to save money on dust collection, all to have a shop full of sawdust and fine particles. I finally realized that none of the cheap-o solutions really worked very well. So I bought a couple of Harbor Freight DC units (about $160 each on sale with a coupon), added a Wynn canister filter to the one I had in my shop (Now sits outside, the other has a bag, but gets rolled outside for use). Have two of the WEN filters, one in both shop areas. Sawdust is no longer an issue. Wear a ventilated filtered mask (Rokler), and when not cutting, wear medical type mask. Looking back, all my home made solutions didn't really work well. The commercial units work very well, and actually cost me about as much as all my ineffective efforts combines. False economy on my part.
After reading an OSHA report on home shop dust pollution, I realized the risks of COPD and other lung problems were not worth trying to save a buck. Serious dust collection may well be the most important tool you have in your shop.
The more I do, the less I accomplish.