My 10yo son has dyslexia/dysgraphia and he has every single one of those symptoms except for the speech and organizational issues. So yes, it sounds to me like your son might have dyslexia and/or dysgraphia.

My sense is that you should test him now, especially if you think the current school will write a strong IEP. But if he's not behind, it's unlikely they'll give him an IEP. My son has a 504. His accommodations are: using a computer to type, extra time on tests, teacher handouts instead of copying from the board, allowing verbal assessments of knowledge if requested, allow use of scribes or dictation (meaning I can type what he tells me to type for homework), not counting off for spelling except on spelling tests, grading for content instead of "looks."

As for switching schools with an IEP-- what problems do you think that would cause?