When we had the private testing, I just called a children's hospital in the area (check their websites, it will say if they do learning evaluations or you can call their psychology dept and ask, usually bigger children's hospitals offer this) & asked if they did learning evaluations. That is the testing for learning disabilities.
The downside is that it is not covered by insurance, any insurance but the hospital here had a deal where if you pay all at once, they take 50% off. I did pay it all at once & it cost me $325.
They did all the same tests that the school district did. I have 2 children with learning disabilities. One tested by the school & my youngest dd was tested outside the school. I had my youngest dd tested outside of the school since they were being morons (common with special education issues) and issues with my ex. It was easier for me to just pay the $325 that get into a legal battle with my ex that would have cost a lot more & taken too long.
Mom to my girls ('94), ('99) & ('02)
And my little guy (12/09)