Any skinning of the framing with ply wood of reasonable thickness, say 5/8" plus 3/4" even better, will add substantial rigidity to the frame on that face where it's attached.
Sheet rock may add some but it's not as sturdy as ply wood.
And, if you're skinning the finished surface with sheetrock use the green board that is mold & mildew resistant.
I think I'm going to go that route, rather than attempting to create some sort of 'removable' supports for the middle. It seems like a reasonable alternative.
The front and one side will be done in green board (I know I said drywall, force of habit...haha) because they will actually be part of the wall that encloses the tank.