This paper presents a theory, based upon the tube model and the random phase approximation, for calculating the scattering from a stretched melt of partially labeled polymers and copolymers. The new feature of this theory is that it includes the effect of elastic fluctuations and inhomogeneities in the entanglement network of the melt. It is already known that such inhomogeneities give rise to the "butterfly" patterns seen in deformed networks and strongly bimodal melts. Here we show that they can also have a strong effect on the anisotropy of the correlation hole peak of a deformed branched block copolymer by coupling to the motion of the relaxed chain ends. By comparison with recent scattering data from melts of H-shaped polymers, we show that previous difficulties in fitting these data can be largely (but not wholly) overcome by the inclusion of this additional mechansism. We discuss the remaining discrepancies with data, indicating where theoretical developments and further experiments are required.