Bracing it would be some work, but it is possible. I would start with some 2x2s and make a framework for the top and bottom. Cut a piece of 1/2 inch plywood to overlay the bottom framework so you have a level bottom again, or you could also just forego the bottom framework and use 3/4 ply. I have included a REALLY rough paint drawing to demonstrate it visually. The black outline is your stand. The red lines would be the 2x2 top (and bottom if desired) frameworks. And at the points where I made amorphous yellowish squares is where I would place 2x4 supports. Put some diagonal braces across the back, and some 45 degree braces on the tops of all the 2x4 uprights. If you are still worried structurally, you could double up the 2x4s.
Normally I wouldn't worry about going to such lengths for a stand made of press wood, but it really seems to go with the tank well. Only you can decide if saving it is worth the effort.