How can I add support for my floor inside a rigid metal return vent?
One option to consider would be a set of pillars under each individual floor board, wedged or glued firmly in place, perhaps only secured on the bottom to allow for thermal movement. 

This concept extended within my grey matter to suggest a plank running across all the floor boards, but with holes across the span to provide for the airflow.

The pillars could be hardwood dowels of an inch diameter or larger, or strips of lumber with the grain oriented for maximum support.

A plank with holes would be more restrictive, but having more than one option isn't a bad idea.