I did this 4 years ago. The training centre (school) had to write a conversion proposal to local authority, which the authority had to approve. It involved a bunch of flight checks and the flight exam (similar to what you did ab inito). I suspect there might be an easier way, but that's how I did it. I understand the school was trying to make some money from me this way, but I needed to convert and they were the only ones who bothered helping. Other training centres weren't interested, presumably being too busy milking their their integrated ATPL cash cows...