Newly diagnosed

As many as 75% of autism cases are caused by folate receptor alpha antibodies.

In this case, a milk-free diet can improve symptoms.

A milk-free diet downregulates folate receptor autoimmunity in cerebral folate deficiency syndrome

Cerebral folate receptor autoantibodies in autism spectrum disorder

Folinic acid (not folic acid) treatment has also been shown to improve symptoms.

Folinic acid improves verbal communication in children with autism and language impairment: a randomized double-blind placebo-controlled trial

An elimination diet (eliminate wheat, corn, peanut, sesame, soy) can help for the following reasons:

The role of glutamate and its receptors in autism and the use of glutamate receptor antagonists in treatment

Arumugham V, Trushin M V. Autism pathogenesis: Piecing it all together, from end to beginning ... . J Pharm Sci Res. 2018;10(11):2787

https://doi.org/10.5281/zenodo.1477515

There is another thread in here on first page about someone who is fine at school but melts down at home - worth reading and I’ve responded from my experience there. 

More broadly though, you might need to reasses some of your expectations of him. Although having a tidy room and teaching self care is important, really is it so important? Maybe focus on the stuff that is vital and let some things go. It’s been so hard for us to “not sweat the small stuff” particularly as it just looks like “bad behaviour” and also we don’t want to have double stabdarda between children. But they are different. We try to treat them fairly but that doesn’t always mean the same. 

The best advice we ever got from someone who was supporting us with parenting strategies for children with autism was - if you see behaviour you don’t like, you need to keep asking yourself two questions: 1. Is it really a problem? 2. Who is it a problem for? If it’s just affecting you and it falls into “irritating” rather than “dangerous” camp then you might achieve more of the important things by choosing your battles. 

Does your son have any way of safely venting all of the stress & anger that builds up within him? A punch-bag or similar may be something he can burn off all his energy without destroying everything around him. Does he have anything he can look forward to each day that gives him something nice to focus on? Does he have any hobbies that de-stress him? Even walking a dog can use energy and give him focus.

Along with what Plastic and Gin900 have very well put, consider also reading THE COMPLETE GUIDE TO ASPERGER'S SYNDROME as a book or for free via this PDF link:

http://www.autismforthvalley.co.uk/files/5314/4595/7798/Attwood-Tony-The-Complete-Guide-to-Aspergers-Syndrome.pdf

It covers every stage of pre-adolescent and adolescent development, education needs, work a-rounds and resources. It deals with adult needs and considerations also, but not as in depth, although it does have a reasonable amount of references for the mature (or in your son's case maturing) autistic reader. 

I agree with above- when he comes home, he needs to release the stress that 'coping' with school causes. Take it from someone who has masked most of her life. I'm an adult, but lists, charts and routines are really important - a picture chart/list of tasks with the daily 'duties' he can do may help. I put things for myself on the fridge so I can see what needs to be done every day. You being ultra calm is very important. Meltdowns are not pleasant to see I guess, but sometimes he will need to discharge- a soft, safe place is important and allow him to shut down and re-charge before it gets to meltdown. 

Have you considered that when he comes home he's had a stressful day fitting in. He's probably frazzled inside.The world gets more stressful as we get older.

You might not realise it but 'normal' people are incredibly chaotic and unpredictably random. Your demands on him may not form a pattern in his mind so you are catching him off guard.

He's probably 99% stressed from school so he needs time to discharge before he can get into 'home mode', so if you accidentally interrupt him, you add the extra 1% stress which takes him over the edge - you will get the full force of what he can't discharge at school.

You might need to look at your own home routines and try to get some simpler structure in place so he can predict his environment better. Maybe even write down an agreed rota so he knows what's expected and that he can see it's fair - and that everyone gets policed the same way.