I think it would help if they/you could work together try to pinpoint the precise triggers. Obviously it may just be sensory issues but not necessarily.
At DS school they have a quiet area where he can go if he feels overwhelmed (so helping to avoid total meltdown). This is where Cahms have come in with a nurse who has done a few sessions with DS on recognising the feelings, physical reactions that take place in an anxious state. She says the these strategies can be adapted according to the age and understanding of the child.
You can also find visual charts which enable you DS to point to where he is (happy, calm, angry) or identify his place numerically (five point scales--take a look on Amazon/ebay). You can get little cue cards which your DS might be able to use (which basically he can use to tell an adult he needs some quiet/time space).
They use a visual timetable and make sure he knows what is happening and when (I got DS a watch to help with this). If they deviate, as they sometimes do, they will explain it to him.
They make sure that the instructions they give about anything that needs to be done are as clear and simple as possible and that there is someone (TA or teacher who makes sure there is no confusion).
There are a few other things that have come to light with DS that never occurred to me before this process. At assembly the noise and crowds can be too much. At carpet time he likes to sit at the back. Since the teachers sound as if they are trying to help perhaps they could also think about how he inhabits the classroom/playground space as well.
The clearest explanation I had for the meltdown was in a book that used a computer analogy: Most people run on Windows but there are some who operate according to an Apple system. Input designed for Windows people won't always work for Apples and can cause a short circuit effect. Trying to add more Windows input just makes it worse. You need to step back, allow the Apple time to cool down and then maybe you can think about what happened (triggers, incompatability). The good news is that some clever people might be able to work together to find programmes (interventions) that work to enable Windows and Apples to communicate effectively.
I hope this helps (I'm rather new to this since DS has only had a diagnosis for a few months). I have found Mumsnet SN board and the archives to be absolutely fantastic, though, both in terms of interventions and understanding ASD as well as the other things relating to statements and so on.