I ran some numbers through the
https://woodbin.com/calcs/sagulator/. Your stand members look to be 2x6 doubled up and the tank weighs approx 3000 full. If the tank is 8ft x 2ft the deflection of the front support is only 0.03in , if 10ft then only 0.05in, without a brace. The addition of the 3/4 plywood does increase the support strength. This amount of sag will be noticeable to the eye but would be temporary. I would still recommend draining the tank to reduce weight before accomplishing the swap.
My 260g (7ft x 30in x 24in) sits on a frame built of 2x8 doubled up with 3 layers of 3/4ply but the tanks has 100lbs plus of gravel and lots of large rocks so similar weight to your 300g. I do not use a center brace.
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