In CA we have a collection of Diagnostic Centers that are really useful for teasing things out.  Not sure if they have them where you are.  They pull together a multidisciplinary team to assess a child.  Depending on the referral question, that could mean speech therapist, geneticist, developmental pediatrician, clinical psych, school psych, etc.  And it's F-R-E-E to families.  

The catch is that referrals can only come from the school members of an IEP team.  Parents can't refer their kids, though they can ask the IEP team to refer.  It might be worth calling a school psych in your district to inquire if such a service is available.  Here, the Dx Center will only consider a referral if the district has performed a complete assessment first -- the district needs to have exhausted their diagnostic capabilities.  But for an initial IEP, the parents can always refuse to sign (which disallows any services, but also doesn't place your child in special ed).