I understand that.
Even with our "fairly" universal health care... we ended up in the same position.
But even with an umbrella diagnosis... there is a tendency to ignore some of the medium-sized related issues, like Auditory Processing Disorders (APD). Here, if the school sees "Autism Spectrum Disorders (ASD)" as a diagnosis, the other problems get ignored - totally. Every behavior challenge is than labelled as "he's just Autism Spectrum Disorders (ASD)"... not as a flag for some other challenge to be accommodated.
There are no "good" solutions to getting the right help in a timely and affordable manner... anywhere!
(if the parents on this board ran the world... <grin>)