Full disclosure: I am autistic (Asperger's syndrome) and I have fought hard not to be the guy you are describing.
BE BLUNT, BE DIRECT, BE FACTUAL, STAY ON POINT
We have a great deal of difficulty understanding why something that is true (or something we see as true) would cause offense, so trying to make a "how would you feel if..." style argument would likely result in "I would feel that they respected me enough to tell me the truth".
understand that you are dealing with a neurology that does not work the same way as most people's
Someone with autism is often confused by niceties.
You might say:
I think you may want to consider softening the tone of your emails
The autistic person will break that down into all of the logical statements.
"I think" (okay, this is an opinion)
"you may want to consider" (YOU DON'T KNOW WHAT I WANT)
"softening the tone" (what's wrong with my tone? There is no tone, I'm just telling the truth!!!)
see the problem?
There are many experiences/feelings that someone with autism has a hard time relating to, just as you cannot relate to what causes an autistic meltdown.
Now, while the following might be considered rude by most, an autistic person will appreciate the factual nature and bluntness.
Dave, in the future, you will direct your criticisms to me, and ONLY me.
Do not try to explain how others feel, do not try to tell him what is wrong.
Tell him what you want, be blunt be firm.
Many of us with autism don't even understand our own feelings so we certainly won't understand the feelings of others.
Back to this point:
he continues to criticize people publicly and thinks he is right, he doesn't see the harm.
You may want to give him a copy of "How to win friends and influence people" because that was a godsend to me. It puts forth rules and details as to WHY the rules work.
He doesn't see the harm because he has no frame of reference. You need to put it in terms that make sense to him. Either the book I mentioned above, or a simple.
Dave, I want it done this way. If you don't follow this instruction, you are not doing your job. I am holding everyone else to the same standard and I will not make an exception for you.
Finally, don't let him hide behind his autism.
A diagnosis is not an excuse
We all have to live in the real world, letting him get away with behavior that hurts the team will not help him or your team.