It turned out to be a bugger to cut so I abandoned the project. But last Saturday I again saw an example of a doormat field and so redoubled my efforts.
And it all started to unravel...
I might still be able to make something out of it, and started seeing how well the bits glue and look. Maybe some promise as brush markers and such, but not sure I need them. Worse, I now have to store an unravelling mat.
The solution is to look for a doormat with a rubberised backing which was the type I saw on Saturday. It means a trip to Ikea.