My 8 year old son was diagnosed on the autism spectrum last…

Hello,
It sounds like you are trying many things in order to provide your son the support he needs in order to be successful. Your question seems to be twofold - 1) how do you support your son so that he can make progress and 2) can someone have adequate social skills and still have autism spectrum disorder. I will do my best to answer those for you.
1) Diagnosis is based on a list of symptoms and usually treatment is geared to target those symptoms whether it is through therapies, supports, or medications. Unfortunately people get fixated on the treatment of the symptom and don't always consider the overall implications for the individual. Schools will often argue against therapies that the test scores do not support even though they may be a benefit and help with integrating the skills. As an advocate I argue educational benefit if the school performance/behavior/social-emotional indicates a need for the services and the test scores do not.
Although the developmental pediatricians in your area specialize in ADHD, they may be better able to assist you with your options for your son because of there unique training and background. In order to address issues of behavior within the home, you may want to consider applied behavioral analysis (you didn't mention this as something you had already tried). As with any professional, do your research and make sure they are a good fit for your son.
2) You mentioned in your post that your son is sociable, but he dreads Saturday because it means he must play with his friends. Autism and Asperger's are part of the Autism Spectrum Disorders. They are considered to be on a spectrum because, while there are some stereotypical similarities, no two cases present exactly alike. It is possible for an individual with ASD to be sociable and still prefer to be by them self. For example, in my clinic, I have worked with individuals with ASD who can carry on a conversation, maintain appropriate eye contact for the duration of the interaction, and ask questions of their conversational partner. The main thing that I noticed in these conversations was that, even though the individual was demonstrating good social skills, they were able to maintain as long as the conversation remained on topics of their choosing and they would often guide the conversation to their preferred interests. They also would avoid social situations if allowed to.
Remember, you are not alone. Try to connect with others in your area and support groups that can help guide you to the answers you are seeking. I hope this has helped.