BT don't manually set your target noise margin higher. It's the automatic DLM process which does this when the connection is seen to be unstable. The same process can automatically reduce it when the necessary criteria for stability are met. It's not entirely clear what these criteria are, and reducing the target noise margin will take some weeks even if it happens at all. They can, after some persuasion, reduce the target noise margin or reset it to 6dB, but they don't like doing it, for what are generally quite good reasons - i.e. if the conditions which caused the original instability still exist, then DLM will soon increase the target noise margin again to stabilise the connection.
In reality, your best bet may well be to tweak the target noise margin in the router, and accept that you won't be able to get back all the way to the position you were in before.