That top bracing will work fine to support the long panels. The only thing I see is that the corner seams are unsupported and are the weakest part of this tank. I'm assuming your tank is around 20" tall, so your 3/8" glass is skimpy for an unbraced corner, which amounts to a rimless design. If you're going to have issues, it will be at the vertical seams.
It would be fairly easy and cheap to acquire a couple strips of 3/8" glass to "cap" the ends of the tank and reinforce the corner seams if you so desired. Just make sure to use an aquarium safe silicone and allow to cure completely before filling the tank.
For the bottom, I would just cut a piece of foam insulation to fit and place it between the tank and the stand. This will protect the glass from contacting any hard parts of the stand and help to eliminate any pressure points when the tank is full of water.
None of these solutions are particularly elegant or pretty but will amount to a more reliable tank. If you want to add your own trim, look into outwater plastics on amazon, they sell corner trim that I've used on my tanks before, but they are relatively expensive imo.