Go for the IEE, klmno. You have too many unanswered questions to accept their report.
Past information is very helpful to evaluators. However, preconceived opinions do not help much when you're trying to find out what is going on today, whether there's been progress in areas not clearly visible to the observer, regression, etc. Also, the evaluator should be savy enough to make these Recommendations in his/her report.
I don't mean to say that brainstorming and working with-sd personnel is a bad thing. But there are clues and some disorders that should have automatically been considered for your child -- like a planner, teaching time management skills.
Just so you know, your sd has a list of the accommodations that are pretty typical for some students to need. (Our sd list has about 40 listed.) And accommodations your child may need are not necessarily "listed" on a list. And students do not typically need every accommodation imaginable.
If this evaluator is so inexperienced as to not know about accommodations or know that your child needs them, how can one place validity in the findings?
They are just trying to appease you and get out of paying for the IEE in my opinion.
Either way, I'd want an unbiased opinion(s).
by the way, don't let them limit the IEE to a specific area.