@fBoyle-- I'm not an expert on this therapy, but as far as I understand, it's not really the singing that helps, but rather the rhythm and patterns.
My uncle developed speech problems after a stroke and he received melodic intonation therapy. He can now form simple sentences without any trouble. In the beginning he was singing them, but now he can say them as is.
The only downside of melodic intonation therapy is that it is not available everywhere. My uncle had to be driven an hour away for his sessions. I wish therapist could visit patients at home. The other option could be to train family members and have them apply the therapy but I don't know if this is possible.