Smart targets = specific, measurable, achievable, realistic, time-based. In other words, "by x date he will be able to read any CVC word on sight."
Many people refuse to test for dyslexia before year 3 because many of the symptoms are things that many children do before that age, then as they develop non-dyslexic children stop doing them.
Ed Psych visits are like absolute gold dust for schools in our area - I don't know what the rest of the country is like but I can't imagine it's much better. Our SENCO has had to plead with our EP to see a year 2 child whose reading & writing is at 1c, so if your son is at 2c he certainly wouldn't get seen round here.
You need to pin the school down on strategies they'll be using to help him recall and write down facts and ask them to tell you what you can do at home to support him. It's in their direct interests to get you supporting him in the way that they are as their strategies will be far more effective that way.
You describe him as reading the words on the page but not processing them through his head. That suggests to me that he's not comprehending what he's reading - not taking it in. My solution to that (if he was in my class) would be to talk, talk, talk about what he's reading. Read to him and discuss the book you're reading. Get audio books for the car - stop it at a cliff hanger and then talk about what might happen next and why. Ask the school for suggestions of questions you can ask when discussing books with him - I have lists I give to parents.
And DON'T get guilt-tripped into paying for a tutor. 10 minutes a day with you will be far, far more effective than an hour a week with a tutor. Can your DS sequence stories or events? I sometimes photocopy pictures from a book and then ask the children to put them in order - can he identify beginning, middle and end of a story he's just heard? His teachers really should be helping you with this. Don't feel guilty asking them for more guidance - it will make their lives easier in the long run if you are supporting him effectively at home.