Well done for continuing to support your son, even though it sounds very difficult. I was relieved to read that he is willing to see some therapists, because it is he who needs to be able to discuss his 'stuff' with someone and you can't do this for him, despite how much you may love him. I am hoping that your son may consider seeing an EMDR therapist - this stands for Eye Movement Desensitisation and Reprocessing and I believe your son would benefit dramatically from this therapy, given the situation that you have described. This therapy is based upon the belief that when we experience a highly emotional experience, even as a child, the subconscious mind can absorb beliefs about ourself and/or the world that are often unknown consciously, but which can have a very powerful effect on the life, which is distorted to fit withe these beliefs. For example, it could be that your son truly believes that he was abandoned, because his young mind at the time of you needing to go to work was not skilled enough to recognise that you were in fact working to give him a better life. When his father left the home, his beliefs were strengthened. It sounds also that he is living under some kind of 'what's the point?' belief - so nothing is ever done, or is ever worth the effort. It really isn't useful for me to guess what his beliefs are, as they are his alone, but I am using these examples based on what you tell me and to give you an explanation.
Usually we process away the anxieties of the day at night during REM sleep (Rapid Eye Movement) but when the memories are so strong, they are not processed away in this manner. They remain lodged and are triggered in daily life, so the person re-experiences the pain from the past. This is why he continues to blame you - he is talking on behalf of the small boy who has not yet applied his adult mind to the situation in order to understand it. This DOES NOT mean it is your fault - it is simply how children can misinterpret your good intentions in their young minds.
EMDR can be an emotional therapy as your son would be asked to go back to some situations in the past in order to process them away, which means that although we cannot change the past, we can let go of the emotions and other baggage that are intrinsically interweaved with the memories. This leaves the future looking much less distorted and more positive. However, it isn't a talking therapy and your son would be able to do most of the work in the privacy of his own mind. It might sound a bit crazy, but I would definitely recommend it for your son. Have a look on the website www.emdr.com for more information and to find a local therapist. I sincerely XXXXX XXXXX both the very best with this issue. Best Wishes, Sarah