that does not add up, when both families entered in August on a single entry that got extended.. The permitted to stay date is 4 months apart on the extensions.. Maybe the letters from the schools where different. Could be a typo in the letter, or a mistake from the IO. If the school terms is the same it has to be a mistake somewhere.
I mean it says that you can work anywhere. It does not explicitly say you can change completely to a new employer, but it also doesn't explicitly say the opposite.
.. I am not saying you are incorrect. But I personally interpret the text differently. Do you know for a fact from the Thai website that what you say is correct, or is it your "safe" interpretation?
Being allowed entry, in however form or shape is always at the discretion of the particular IO you hand over your passport to. Be friendly and polite, and its not out of the question to ask for something. I also had friendly IO's (thai and laos) sqeeze in exit and entry stamps in on otherwise full pages in the middle of my passport, because I only just had two full pages left when I went to Laos to get a SETV, where the Laos visa and TV alone takes two whole empty pages.
There is no requirement to stay any length of time. Just go around the building after stamping in to Laos, and stamp out again, take the bus over the bridge again and stamp in to Thailand