Tod, there's better than that. If you pay 30,000 baht every 4 months, you literally don't do anything. No school, no immigration, nothing but sit on the beach all day.
It's beyond me why people bring children here to be educated in the first place.
The majority of expats I've known throughout the years, take the children OUT of Thailand and back to the west to get a decent education, unless you can afford the hundreds of thousands of baht per year for the very best schools here.
There are outfits running, that charge other fees on top of the extension fees.
These 'Schools' are simple to find. The costs over a year, can mount up to not far short of a yearly TE visa fee. Of course people choose that route due to the fact that they don't have to pay 5 years up front. It's all illegal of course but people do it simply because they can.
I'm not saying this is what the OP is doing but 100% the schools are out there to do it if that's what you want.
There's a lawyer that often posts on the Darkside forum who works alongside the British Embassy and in IDC. He's under the opinion that appealing a decision is a waste of time. Once they have decided to deny you entry, your not coming in. He states the appeal go's to the senior immigration officer who made the decision to deny entry. They mostly won't revoke there decision.
John West 're a new passport. I think your a little confused. You can request a new replacement UK passport at any time. They will add up to 9 months to it making it 10yrs and 9 months validity providing you have 9 months left on your old passport. If for instance you had 6 months left on it, they would add 6 months making it 10yrs and 6 months on your new passport.
If you applied now, your new passport would be valid for 10yrs and 9 months.