Re-analyze the joists to see how much they are falling short of the required size, for the deflection limit you need. This should then give you enough information to size your plates. Or (cheaper option), if simply sistering the joists in that area will be enough to cure your woes.
Just for clarity; what size are the existing joists? Picking through the dimensions in your post it looks like they're 4" x 8" x 8' 6" long.