The plywood is already supported on both sides. The sag is in the middle, where there is no support. Right now, the sheet of plywood is being required to support the weight across a 5' span, and it's clearly not up to the task. By supporting it in the middle of that span, the span gets cut in half. And it's much simpler to do.
I'll use a 12" piece of 2X4 with a piece of wood on each end, roughly 8"X12" to spread the load. 4 angle brackets, 2 for each board to attach them to the 2X4, and should be good to go. Whole set up should be about $5. Less if I had access to my garage back in Mass.
If that small investment in time and money don't solve the problem, then I'll go the angle iron route, and hopefully by then everything will be moved to the new home in Fl.