There is cross bracing only every 4 feet. As a first step, I would add cross bracing at every joist. This ties them all together so movement is less noticable. It can make a big difference. I would use 1x4's cut at the correct angle for your 12 inch centers, attach the top with liberal amounts of PL400 and glue/screw the bottoms. Solid blocking would be good too, but is usually difficult to install because of the uneven spacing and warping of the joists. For your 16 foot span, I would put cross bracing at the center and 4 feet either side of center.
The plywood attached to the bottom would add stiffness, but the cross bracing should be done anyway before the plywood is installed. The plywood attached at the bottom would turn the joists into a form of I beams, this is the method used by some prefab home manufacturers, and it does work.