perhaps this is a Chiang Mai thing? I recently had a full passport with many past stamps and extensions in thailand and they only moved my original non-o and my last extension stamp, nothing else.
it's going to be interesting to see what immigration does with these DTV visas once they start coming up for renewal. It may be the case that you have to visit a foreign embassy on every 180 day bounce.
Thai language schools and Muay Thai gyms that provide classes for people on education visas typically handle the paperwork for you. Find a school, ask them, and they will sort you out. Most can get you from a tourist visa to a non-o, no problem
1900 baht at any immigration office in Thailand... pretty cheap, but you have to do it yourself and have the correct documentation including the 800k THB in a bank account sourced from outside Thailand. Or you can pay an agent to handle that and everything else for you, but it's a lot less cheap.
then you may need a lawyer to fix it all up for you. Certainly possible, just how much hassle is unclear.
It sounds like yes very much you can do what you want, buy property in your child's name and live in thailand. You'll be doing yearly extensions to a visa and 90 day reports and all that, and you can't sell or mortgage the property... but you can do it I think