There's no such thing as a 1 year non-O. Non-O visas are all 90 days.
If you want more time than that, you go to your immigration office and ask them for their list of requirements to apply for the 1-year extension. Then you apply for the extension based on their list of requirements. Then you can purchase a re-entry permit for the extension. You would have to extend every year. Likely by showing 800,000 baht a bank account in Thailand.
If your immigration office supports in-country conversions to ED visa then you can just leave and return and go to immigration with the proper paperwork.
Just be warned there are many reports of some Bangkok Bank branches refusing to provide the letter for monthly transfers. I've seen most people resolve that by going to a different branch and getting it there.
You don't have enough time left on his stamp to do anything. Converting to another visa requires a minimum of 15 days.
You'll need to leave Thailand and re-enter to get your son a new stamp. Then you can work on getting the new visa. Or you can apply for the visa through a Thai embassy while you're outside of Thailand.
Why were you using an agent? Does his school not support education visa applications?
Only thing you need to be careful is the requirement that your bank account can never drop below 400,000.
So the safest way to make this move is to keep 400,000 in BOTH accounts for a few days.
That means if you have 800k in Bangkok Bank, transfer 400,000 to your Kasikorn bank account and give it a few days to settle there. Then you can transfer the other 400k over.
If you just keep 400k in your Bangkok Bank account during the middle months, deposit a new 400,000 into your Kasikorn account and leave it a few days before withdrawing from Bangkok Bank.
Make sure you do this soon, before you hit the 2 months before you will apply where your accounts is required to be at 800,000.
Note for your extension that you'll need to provide the bank letters and 12 month bank statements for BOTH bank accounts. But next year you will be able to just use your Kasikorn account.
You can apply any time you want to convert from visa exempt to non-O, but must have at least 21 days left on your entry stamp.
You cannot apply for extension after 30 days. You would need to wait at least 45 because in Chiang Mai you can only apply for extension during your last 45 days.
Make sure you're aware if you have Bangkok Bank that if the money you're going to use for visa/extension has not been in your account for 4 months already on the day you ask for the bank letter, they'll require you to sign something freezing your funds for 4 months from the date the letter is issued. All funds in the bank at that time will be frozen for 4 months.
Getting the visa from home saves you at least 2 trips to immigration. The first trip to apply for conversion and the 2nd trip to pick up the visa stamp after the under consideration period.
Also if you're applying for non-O based on retirement you must be able to show the funds in your bank came from overseas when applying in country. This is not the case for the extension.
NOTE: No immigration office in Thailand allows you to apply for trailing spouse visa. You will not be able to get a non-O visa for your foreign wife based on your visa. She'll have to qualify for her own visa. I don't know of any embassies in the world that still allow for this either if you have a non-O visa. Some do still allow it if you get a non-OA visa. But then you have the insurance requirement.
You cannot extend a non-O visa for 1 month. You can only apply for the 1-year extension, unless you're married to a Thai (then you can do the 60 day "visiting Thai family" extension).
There's no simply way to get 4 months in Thailand without doing a border bounce. For the least amount of hassle, suggest getting the non-O visa from the embassy, and just doing a border bounce and returning visa exempt after that.
You're correct. No need to do anything except exit Thailand. It's only long-term extensions where an upcoming extension is planned that really need to be transferred.