I would definitely ask his pediatrician about a DCD diagnosis. My DS10 got this diagnosis at age 7 (based on a different motor skills test by an OT).
Many of the things you mention are very familiar - moving slowly, difficulties with writing, and so on. My DS doesn't have speech difficulties, but I have read that some DCD kids do. ADHD symptoms also overlap with DCD symptoms.
DS was also diagnosed with convergence insufficiency. I was skeptical about the vision therapy (and so was the pediatrician), however he had a lot of difficulty reading so we gave it a try. It was clear during the initial VT testing that he was skipping words, skipping lines when reading. In our case, the VT did help - with both reading and with ball skills - DS can now play basketball tolerably well, where before he had trouble. I thought of the CI as just another aspect of the DCD, by looking at the eye coordination as another fine motor skill he needed help with. I know that VT won't cure dyslexia though - I would avoid any VT that claimed this was the case.
Perhaps look again at the SLP as well - possibly it is similar in helping the fine motor skills required for speech...
