Well, the polygon library has been through a lot, and still remains "almost working", which is about as useful as "not working at all". Once again I can see the light at the end of the tunnel and once again it looks quite a long way off.
So, again, rather than plough ahead in to a complicated final solution I am going to try and sort this with a tried and trusted technique, usually involving pens and beer mats.
In practice the plan is to take some paper and pens along rather than actually use beer mats. I may have to find paper with a square grid on it. But the venue should be appropriate as it is the Great British Beer Festival in Earl's Court, tomorrow afternoon.
I suspect I will get lots of helpful advice from my friends on this problem and I am sure a lot of squiggly lines will be drawn...