Hi! I am new here too. My daughter just turned three and she was speech delayed too. Back in January she only had a vocabulary of perhaps 50 words and now she is doing so well she was released from Early Intervention a couple months ago having met all her goals. The speech therapist wasn't very helpful. We just worked really closely with our daughter and used whatever worked for her (sometimes going against what the speech therapist told us--for instance, our daughter needed to be prompted to talk). But I really think learning to read at the same time as she was learning to talk really helped a lot and helped her to get further faster. My husband agrees.
Our reading times are great speech practice times too.
Oh, the "Your Baby can Read" videos and the "Meet the Sight Words" videos seemed to help because she would say what they were saying and they definitely helped her start reading.
I'm not saying that what worked for us will necessarily work for your little one, but I'm hoping it is encouraging. All the best with your child!