Private school complaint

I would also be tempted to go to the media if you don't get the desired outcome. Having said that, we don't know what it is. What kind of safeguarding issue? And did harm come to your child?

Sorry-forgot to say it may be too late for you now but I would also have demanded a lot more than half a term's fees refunded if the incident resulted in your DC leaving the school e.g.. start with at least a term's fees plus your legal costs (I asked DH and he said he'd have wanted them to refund all the fees paid since the beginning of the school year!)

You lost me at wanting to expose him for being overweight!
Not sure what actually happened, but daft statements will quickly lose you any upper hand!

In regard to safeguarding concerns, you can take them to the LADO (local authority designated officer for safeguarding) to consider. Allegations are taken very seriously!

Unfortunately you will find that private schools have a bad record -generally far worse than state schools- at coming clean on any incidents which could damage their reputation. State schools are far more likely to report matters to the police/local authorities etc. Hence the ease with which so many sex scandals have occurred at private schools in the past-not just at boarding schools but even at London day schools. A friend of mine's DC was badly beaten up at private school recently and the school just closed ranks with teachers and housemaster all essentially lying . You will also find governors of private schools tend to rubber stamp the head's decision and try to sweep things under the carpet. Your best bet is therefore probably to make it clear to the governors that unless your demands are met and appropriate action taken in relation to your complaint you will be forced to make public disclosure (to any or all of the police, local authority and media as appropriate).

Frankly I doubt you'll expose the head in the way you would like, I suspect they will apologise, and do an "investigation" into what happened. If the safe guarding issue is about abuse of any kind to your DS or any other child then the teaching staff now have a legal duty to report it and you IMO have a moral duty to report it gagging order or no gagging order.
Good luck. or maybe is more appropriate I hope your DS moves on and enjoys his new school.

Have you got a lawyer? I have found lawyers to be invaluable when tackling school on tricky issues. Even if you only take advice "in the background" you will be far better informed of your rights.

What do you want to achieve?

I've never complained to that level but in my job (public sector) we get lots of complaints. My advise is for you to decide at the beginning exactly what you want to achieve by complaining; an explanation, an apology, reassurance it won't happen again, the staff involved to be spoken to, disciplined, sacked, some fees refunded (unlikely you'll get that), do you want the heads head on a platter or do you think the police should be informed? The school should have a written policy on managing complaints have you read it are they following it? If not why not? At the meeting present your concerns and evidence and explain what you want to achieve.
I strongly suspect that unless it's a serious safeguarding issue I.e. abuse then the governors will support the head and you'll hear lots of platitudes and you'll hopefully get an apology. If it is a serious sage guarding issue and it appears nothing is going to be done please go the the police, this is the only way this sort of thing can be stopped. Childline will be able to advise you if you're unsure.