Jen, my autistic daughter started reading a year ago. She is twelve. I started when she was about eight, I believe, and taught her just the way you are describing, but it took much longer than for my other (NT) children. For example, we worked on short-A three-letter words for two years. Hannah learned some of them, but couldn’t get the sounding-out skill down. Now, she also has some other developmental delays, so her level might be different from your son.
She still doesn’t really think in terms of putting together sounds. When we stalled out with “sounding out” I began to introduce more sight words and tie them to actual objects in the room. For example, we had an index card with “window” on it, one with “table” on it, one with “chair” on it. I told her each word, introducing only one per “lesson” time. After she had seen all three, I would hide a little toy in one of those places and show her the corresponding card. She would then go find the toy. If she picked the wrong place/read the card wrong, she found out pretty quickly. 
Little games like that, that tied the words to real objects, seemed to help us keep moving baby-step by baby-step. Then one day last December, she didn’t hesitate anymore. She acted like she actually knew the words we were working on. Once she was ready, she took off. Between last December and today, she has read the pre-primer, both first-grade readers, and is about one-third through with the second-grade reader (Pathway readers). Most of the words in those books, I never taught her. She is picking them up from context and very minimal letter sound recognition (like the first letter of the word, one consonant in the middle, and the last letter). So we still have some fine tuning to do and lots of work ahead of us.
I’ve been using some of Charlotte Mason’s ideas at this point, too, to continue introducing new words and reinforcing the idea of word families/letter sounds.
So all that to say, it sounds like you’re heading the right direction. Be patient. As you already know, it can be three steps forward, two and a half steps back. I had no guarantee she would learn to read, but we kept going . . . gently but persistently, and taking breaks when she would stagnate.
Oh yes, one thing that helped me gauge her readiness was how she was doing at recognizing and completing patterns. We would set up patterns with objects and have her finish the pattern. She was stuck on X O X O X O as the only pattern she could recognize for a long time. Once she started recognizing and completing more complicated patterns, her reading improved too. So you might include some pattern games for variety as well as skill building on the side.
Hope this helps a little.
