That being said, I have a 260 gallon with a similar built stand with no centre supports, but I built it from 2×10’s and a 3/4” plywood top. Zero sag after 4 years.
Eyeballing it, and this is by no means saying you should without at least sagulating it, that it would probably be fine without modification.
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You can use this https://woodbin.com/calcs/sagulator/ to calculate the expected sag over a certain span under certain loads.
That being said, I have a 260 gallon with a similar built stand with no centre supports, but I built it from 2×10’s and a 3/4” plywood top. Zero sag after 4 years.
Eyeballing it, and this is by no means saying you should without at least sagulating it, that it would probably be fine without modification.