It is entirely natural and appropriate to be a bit emotional. This is your child, and you care about him.
(Of course, the emotion can be part of the motivation, but it probably shouldn't be the decision-maker for your advocacy efforts, since emotion doesn't always fit well with strategic thinking.)
I've already listed some of the areas I think would be important and reasonable in an independent evaluation in earlier posts. Remember that you have options: an IEE through a school-contracted evaluator, or a PCP-referred medical (neuropsychological) evaluation, with the focus on apraxia/dyspraxia. The latter may or may not include extensive written language evaluation, but it will definitely open up the area having to do with physical handwriting skills and the appropriateness of assistive technology, and can address executive function skills that have a lot of impact on writing in his case and in others, such as some of the ones you have alluded to (idea generation, initiation, organization, emotional self-regulation). You could also do both, in order to get both a proper evaluation of written expression (throwing the pencil does not count as having been evaluated in this suspected area of disability) and data to rule in/out apraxia/dyspraxia.
There are also some things you might try at home to help with some of the stress points at school. When possible, I'd suggest having him use speech to text (or typing, if he's willing to try that) to generate first drafts. I'd also do an internet search for graphic organizers for writing, and try a few different ones with him. One or more of them may click with him. Even better if they have electronic copies that you can dictate/type text directly into. Graphic organizers also help a bit with the problem of forgetting his sentence while telling you, as their design is to work on one sentence at a time, with the cues for each point already there. (Much like an old-fashioned hierarchical outline, but with visual spaces instead of capital Roman numerals.) His teacher is already using a good strategy for idea generation, which is to give him topics, instead of leaving it open-ended. Once he's reliably able to write to a provided topic, the next step would be to give a circumscribed topic area, and help him come up with two or three specific subtopics of an appropriate scale for the assigned writing, and then pick one to write, moving toward independent generation of those specific subtopics.
