That extra beam will do nothing for stability, the one joist is fine for holding the weight, as others have pointed out it's a short span. If your hardwood was installed correctly (perpendicular to joists) you'd be fine however since for whatever reason it's not there is some potential for a rocking effect over the one joist. Again just to clarify the extra beam you sketched in will do absolutely nothing for this issue. That said there's an easy and simply solution, anchor the stand to the wall. Run a horizontal 2x4, or whatever, and screw to to your studs then screw your stand to that. For best results fill your tank half way and insure it's level before screw the stand to the wall.
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