I see his anxiety as much more important than his actual weakness in writing. He has neat joined-up writing, which is just a little slow and painstaking. When he writes by hand he has a tendency to get lost and forget what he was trying to write.
Sometimes kids "draw" their letters instead of "writing" them-- using, in effect, their art skills to compensate for a language-and-motor deficit. My DS's cursive is gorgeous, but sometimes derails his actual thinking-and-writing process if the writing job is itself difficult. Kids who do this tend to wear themselves out on writing tasks, so as they advance in school it becomes more of a problem.
My reaction to his being anxious has been to institute a daily practice regime with the aim of getting him to feel happier about writing by the time school starts next week (more with the idea "get back in practice" than for improving as such). Interestingly he's been pretty happy with this. [ETA what I mean is: even though he's anxious about writing and dislikes doing it, he does see practice as the way to get past the problem. I am hugely encouraged by this.]
I would be encouraged by that too. And, Colinsmum, the tasks you designed are basically the same things we did with our DS starting in kindergarten (he had a poor pencil grip and was generally very uncomfortable writing). Over time the speed-writing task really does improve fluency. We change out the texts he copies when he gets more than 85 characters per minute finished, so he doesn't get attached to any one text.
School gave DS "advance organizers" (worksheets with places to put topic sentence and the supporting sentences) but he was so aggravated at having to write them twice that he quickly learned to keep an organized hierarchy of ideas in his head.
I'm watching this closely in my own DS9; we see this as a mostly remediated issue for him, but it rears its head from time to time...
DeeDee
