This box build is something I'm learning from... I was originally liking the way it looked and turned out. But I was not aware of the 5/8" materials being used, with those large panels and the power you're planning I don't know why you chose 5/8" thickness, the bracing was a decent idea but with the panels so large and whatnot it probably will flex some.... especially once you add power. Even .75" braced with a double baffle would be an improvement and likely be sufficient I feel, I might leave the doweling at the store and use something with more contact area as the panels are so large, Doing that worked well in the last enclosure I did for my ride and its single ply with large panels as well.
Of course, since you're looking to absolutely kill any vibration doubling up the materials will be best since you are keeping the amps where they are.
However you do it those amps are in a less than optimum mounting position... that's for sure. I'm in the same boat mounting-wise but only cause I chose to be.
Sure... I got some vibration, but it's minimal with no actual flex.
Trying to get rid of ALL the vibration might not be possible... so consider that when you finally wrap this up... I did and it's a chance of failure I suppose but one I'm willing to run.