The middle:
Consider left of the adder U and right of the delay Y:
right of the adder is zY, which must be U - 1/3Y so we have Y(z + 1/3) = U -> Y/U = 1/(z+1/3).
So the total middle transfer function is 3z^-1 / (1 + 1/3z^-1).
The bottom:
I believe you are correct (You can get this by looking at it as a DFII transposed structure)
Sum these all up and you have your transfer function.