Other than that you need to continue to teach him correct social skills if you want him to be accepted as an adult. Eye contact, no stimming in public, a lot of physical contact (basicly be a Mamabear) and also explaining through logic whenever he does something socially unacceptable.
Please don't try to stop him from stimming unless he's hurting himself or others. Being regulated and functional is more important than being normal -- some autistic people literally need to stim to be regulated and to manage in the world.
By all means explain to him, when he's at a point of development where he can understand such things, how other people might view his stimming and give him suggestions for how to make his sort of covert if it becomes a problem for him socially and he'd like to keep it on the down low, but please don't tell him that he shouldn't stim in public or try to stop him from stimming in public. And be careful to make sure he knows there is nothing wrong with stimming -- don't make it out as a bad thing because it's not; It's merely something different, and people are not always comfortable with with difference but that doesn't mean the difference is bad or should be hidden.
I stim a lot (I rock and have a hand stim) and I've been accepted in vocational, academic and personal settings, regardless. (In fact, the first time I was made aware of the fact that I rock a lot was in a staff meeting. It has been a non-issue for me. I am probably a lucky exception to the rule, since many are made fun of or ostracized for such things....but I'm sharing this to illustrate that it's possible to succeed and be okay even if you are visibly weird.)
Same thing for eye contact -- eye contact can be painful/extremely distressing for some autistic people. It can also (for people like me) prevent an autistic person from actually being able to listen and process what people are saying if they get distracted by making eye contact or trying to process all the visual information from someone's face/body language at the same time as processing all the auditory information in someone's voice plus the words they are saying. So again, teaching hm that people expect eye contact and encouraging him to make eye contact to the extent he's able without any harm is great, but I don't think you should force it or make a huge fuss over it.
Teaching him the social value of handshakes and how to be polite about not wanting to be touched is good, forcing him to be physically affectionate is not.
Other things that adults did that helped me:
Work with him on empathy and perspective taking from his point of view -- compare his experiences to those of other people to help him understand how they might be feeling.
Teach him social scripts for things like introducing yourself, asking if you can join in a game with other kids, and starting a conversation. Make them very concrete and specific (give him exact words he can say, and describe when to say them using concrete examples).
Encourage him to pursue any intense interests.
Give him lots of advance warning of changes, if he has trouble with change.
Accomodate his sensory needs whenever possible.
Make sure he knows he is loved and accepted just the way he is. Parents and home should provide safety and respite from the difficulties he will encounter in the wider world.
Things that would have been useful to me:
Don't shame him for having meltdowns, be compassionate and pragmatic instead. Help him to figure out why he has them, what overloads him/what the triggers are and to pay attention to his internal state. Help him to figure out what calms him down and to practice calming strategies in stressful situations. Once a person has begun having a meltdown they can't just stop -- it's not a chosen behavior -- so the best way to address meltdowns is through prevention.