Have you looked at Aquaponics?
The fish seem pretty happy without a Sabbath.
I really don't wish to embarrass you, but had you gone to the link and read what is there, you'd not have left the comment that you left.
The purpose of the Shemita as explained at C_O's link is NOT to give the land a break, it's ultimately to teach by long tradition of planning and experience how to withstand siege and to provide the knowledge of the terrain from which to fight back.
As is the nature of short explanations, you'd be foolish to think that that is all there is to it. Go to the link and you will see why hydroponics does nothing to solve the problem that is addressed by either C_O or Kartographer.
Just did. Looks very interesting from a nitrogen cycle/water use perspective. I'd bet it would do really well with charcoal as a growing medium. Of course, without a Sabbath you're blowing off the tactical value of remote stocking, and the social value of integrating the poor.