I'm going to try to respond to some common themes above, without conflating children too much. I don't have high hopes!
Grossly, writing involves the mechanics of written output, the language content being communicated, and organizing said content. An individual child struggling with writing could be challenged by any or all of those areas. Working memory affects all of them.
There are assessments for other aspects of working memory, such as visual working memory (usually block span). Subtests include the SBV nonverbal working memory, the Wechsler Nonverbal/WISC-IV Integrated spatial span, finger windows from the WRAML-2.
Other aspects of EF are heavily involved in writing as well.
Here's a nice little presentation on EF:
http://www.nasponline.org/conventions/handouts2010/unstated/nasp_ef_presentation.pdfLots of good stuff in it. It starts with a bunch of neuroanatomy, runs through assessment, and then ends with educational manifestations and interventions. I'll just abstract this slide on EF and writing:
"Examples of EF Problems in Writing Skills
• Poor graphomotor control and lack of automaticity for handwriting.
• Poor organization of written material.
• Poor retrieval cueing or poor generation cueing (idea generation or idea fluency when writing).
• Inability to use multiple self-regulation EF’s at one time (hold, manipulate, retrieve, generate, execute)."
As you can see, different aspects of EF affect different aspects of writing. Working memory is involved particularly in automaticity. Planning can be part of what is termed here "poor graphomotor control" (i.e., motor planning).
And now, in no particular order:
"nothing to get out": this may have something to do with mental flexibility/shift, initiation, or retrieval. Often there are facts and ideas, but the child does not have ready access to them. I compare retrieval weaknesses to a disorganized filing system with lots of documents, but poor file structure. Unless it's a document that is very frequently accessed, (so there's a brute force rote memory path to it), the inefficiencies of the filing system mean someone else often has to start opening drawers (or folders) to cue memory of what is in them, or where to find something specific. You can imagine that if your files are in a big mess, starting a search can feel overwhelming, which relates to initiation. (Think of it as the reason few people want to start big closet cleanouts. Except for those of you with excellent EF!)
stories with parts missing: This sounds very much like an EF issue, with organization/sequencing, working memory, self-editing, and maybe a little perspective-taking thrown in. The examples read like there is a complete story somewhere in the child's head, but it's difficult to re-tell it so that someone else understands it. Cueing with sequencing key terms can help (first, next, then, so, finally). Also cueing with sensory descriptive questions/sentence starters, asking for show-not-tell. Using graphic organizers to provide a little external structure and cueing for omitted sections. Generally, scaffolding that makes the process more concrete and externalized. Paper (or an electronic document) is a great working memory aid. Reading aloud what you've written is helpful for self-editing, as is asking yourself, how will the reader know this?