Convergence issues are really out of my realm. I can offer that my son who could read would pretend he couldn't read for his teachers. He just didn't feel like doing it & was very cleverly non-compliant. He'd ask them what the word was or say he couldn't sound them out. I tricked him into reading for them by sending some favorite books to school. I don't know if this helps.
On the FBA - many schools have ABA consultants under contract & you may be able to get the district to pay for the assessment. They pay for FBAs all the time in my area. Good luck!