Not a medical professional, but, might there be some connection such as motor difficulties->poor sphincter seal->reflux->trauma to esophagus->eosinophils? The same motor difficulties could be behind the dysarthria, dysgraphia, and dyspraxia.
And I saw some citations that mention birth trauma as a possible origin of dysarthria. Kind of like how CP can impair motor functions, but leave cognitive functions entirely intact.
I also saw references that said that the prognosis is quite good for children, with good speech therapy.
