You already have a connection with a specialist in your area, so if you don't get anything out of further conversations with your district personnel, the IEE conversation might be one you could explore a bit with your consultant, in terms of what she might recommend as an approach. It might not require a lot of additional testing, since you already have multiple formal and informal consults stating that the existing data are supportive of an LD.

...pronounced like the long vowel and first letter of the alphabet...