Somewhere I saw some plastic feet for under legs of couches on carpet to stop them leaving dents in the carpet. Flat on top and a bunch of spikes underneath that transfer the weight straight through to the subfloor. Big weight difference between couch and a full tank, perhaps a load of them evenly distributed?
My tank sits on carpet on just the perimeter of the stand and is perfectly stable. Perhaps you could put some long thin strips of wood underneath - they'll tend to sink into the carpet and reduce your wobble. As long as they are on top of, or cross over your joists you should be transferring the load to the joists and not relying on the subfloor.
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