First, nice sump and fuge, great quality of build. I'm a big fan of LifeReef equipment. I used to have that same setup on my old 120.
Second, if you were building for a cube where the corners were supported on that stand, you might be kind of OK. You do need some corner braces or the like to prevent the stand, with weight on it, from racking and collapsing.
Additionally some braces under the top would be required for a round tank. Over time that much weight supported only by a horizontal sheet of plywood will cause the plywood to sag leading to possible failure at some point. Vertically the plywood will carry far more load than a tank a few times the size of yours... but that's not what you're doing.
I think a fix for what you have is probably fairly easy by adding a few 1x oak "joists" under the plywood top (maybe 3 doubled up), and supports at each end for those. On the closed end the support could be just a straight 1 1/2" wide board, and the other end maybe a notched 1x4 glued, and screwed behind the top of the door opening, you'll lose some door height, but it looks like you have plenty. Make sure to glue the joists to the bottom of the plywood top with waterproof wood glue, and at least 1 1/2" #6 SS wood screws, drill and countersink the appropriate pilot holes first.
Now I know you shouldn't rely on screws for shear strength, that's building 101. However, this far along in this build I would assume the calculated risk that in addition to a great quality waterproof wood glue used on lots of surface area, and SS screws that aren't going to corrode in a few years when exposed to moisture causing a failure. Without some further pics this may not even be an issue, you may be able to get some supports under the "joist" supports to carry the load to the floor, that would be best. Under any circumstances glue, and screw everything at a minimum.
The 1x4 support may add enough lateral stability to the side it's on but I'd still like to see some corner blocks on both sides to be safe.
Overall, I don't think these are major modifications, but I do think they will allow you to proceed with your plans, and provide some peace of mind. They'll have a dramatic impact on the suitability of the stand.