I have some similar boxes like those. Mine are only 3/4" thick. 7 cu. ft. is just about right for the LE14A's I picked up last year. Maybe a little big, and the huge panels need bracing. Bracing will shrink the interior volume, I'm keeping track of how much wood I'm adding so I can calculate the final volume.
First thing I did was glue in a liner made of some 3/8" underlayment (particle board) I had on hand. The idea is to dampen the huge walls so they won't be ringing like a bell.
Next I bought a bunch of 2X3's and started cutting them to fit in all the corners, followed by a lattice work all across each panel. Start with a long piece across the middle, then shorter pieces going the other way to form a big "+" on each side. The panels are so big I kept going with smaller pieces to break up each rectangle into smaller ones.
Every piece is glued in and also coated with Liquid Nails so there will be no buzzes or rattles. Also screws wherever possible, just be sure to calculate the length carefully so they don't poke through the nice veneer! I take some pics so you can see what I'm talking about. Maybe tomorrow, It's been too hot here to even venture outdoors...
I'm planning on putting some 2X4 braces between top and bottom and the sides, and a front to back brace or two as well. Those ones have to be bolted to the baffle, hopefully close to the thin spot between the woofer cutout and the tweeter hole.
My baffle board was originally 3/4" ply, I bought a sheet of 3/4" MDF so I could duplicate the outside dimensions and put my woofer and tweeter where I want them. The way my grill is mounted means I could not make it any thicker, at least around the edges where it gets screwed in. I cut another piece that will slip inside the mounting flange though, so it will end up 1.5" thick every where else. It's like a sandwich with about a 1" wide rabbet all around. Have not cut those yet, although I had Home Depot cut the long sides to the correct size, I just need to trim one end of each piece.
The boxes were pretty light when I got them, now they are getting to be a bear to move...