Wow there you have it. Super bit of detective work. The original course of the Rae was up the page sans the floodgate being put there. There was probably a minor rapids at that point and higher ground to the right. So they dammed the rapids and forced a flooded area to the right as shown and this water would have been held back by the Heathmill dam/weir on Fazeley street. All of this would have raised the water to the height of the floodgate penstock and in so doing the river would have been wider and slower running up to above Digbeth bridge. There were boats on it apparently and occasionally Lloyds mill may have been affected by levels too high in the tailrace which would stall the wheel. Also wagon traffic had difficulty crossing the Rae at Derrittend. I'm not sure if Lloyds wheel was affected; the problem may have been traffic crossing the Rae to get to it. Anyway, downstream measures had to be taken to prevent this from happening. When the Heathmill was no longer viable, they simply removed the dam at Fazely street and allowed the water to run off. The floodgate dam was maintained seemingly and the water was allowed to follow the man made run/leat by the remains of the old mill...albeit at a lower level and as you point out the narrow stream again. In the drained pool area, immediately above Fazely street; the Gulverton tin factory was built and a couple of steelworks above that on River street. All of this would have been the wide flooded pool for the mill prior.
The included portion of Westleys picture shows the Heathmill dam and mill with two wheels. The road past the house would become Fazely Street and there is a horse crossing the damm...the widened river to his left with some fishing going on. The full picture shows the water up to Digbeth bridge and the floodgate and it has an island in it. I think the house on the right still remains in modified form as part of the Bond buildings. I have posted this before the wipeout...maybe there is some interest in tying it all together and the last little map adds another link in the chain.