Should be doable... Boxes come apart easier than most people around here like to act like they do sometimes.. Get a razor blade with a handle, remove all the screws and shove that blade into the gap and it should come loose a bit.
If you want to check if it's resonating, crank it up on some music with a variety of high and low tones and see how she hold up. Real low tones and real high tones tend to work the best.. Things around 20hz and aroudd 60hz, IME. On the high notes you shouldn't hear any nasty buzzing, if you do brace your longest panels with your hand and see if it goes away a bit.. On the low notes, you may find the wood on the larger peices bends or buckles, just placing your hand lightly on the top will allow you to feel what type of stress it's under.
Box building IS FAR from my forte.. It took me quite a while to learn how to make things that were 100% structurally sound.. Most of the big SPL guys use 5 layer boxes no bracing, and trying to implement that in a daily driver doesn't work well. Had to learn that the hard way, also I don't have all the tools I need so the cuts aren't always perfect.. I've had to do a lot of build, rebuild processes before.. Haven't had too many issues in the last year or two, but trust me, I used to have issues like this often.
Anyway basic rule of thumb is if it's 3/4MDF you need some kind of bracing for every 12 inches.. So you should have 2 dowels on those longer sides.. You could throw a couple panel style braces along the walls fairly easy. Take some scrap 3/4 mdf and basically double layer the box for about 4-6 inches running along each side of the dowls along all your long walls.
