Its 7 metres away and the planners are still getting worried about overshadowing? Either there is something about the site or there must be another agenda at work here. From your description I am starting to suspect the latter. You don't mention what your designer is doing, he really needs to pull his finger out and come up with a strategy to tackle this.
If all else fails take the rejection and go to appeal. Mind you by then the neighbour probably would have sold and the objections will melt away.
If all else fails take the rejection and go to appeal. Mind you by then the neighbour probably would have sold and the objections will melt away.