If I was a planning officer and that was my job, I wouldn't be bothered that bothered about the 45 degree rule as it doesn't oversail the lines dramatically.
Then you would not be doing your job properly
The council has published policy stating that the 45 degree rule will be applied. There is no justification for the rule to be relaxed in this instance other than the OP wants a big extension.
The planner must enforce their own policy, or have a very exceptional reason not to. Wanting a big extension is not a reason
As a planning officer, your job is to look after the interests of the neighbours too, and perhaps the neighbour does not want a big extension next door blocking all their light