as I said previously, there is no "converting to non-O." If you start with the ED visa then she's already on non-immigrant status which is the entire season for getting the non-ED. She can't convert to something she's already on. You would simply be changing the reason for her extension from education to trailing spouse. There is no visa involved at that point.
a second entry wouldn't be an issue. It's also much more about how long you've been in Thailand than number of entries. If she goes to Vietnam a month after you arrive to Thailand there won't be any issues getting back in
if your wife has a NZ passport she can enter Thailand visa exempt. If that's the only thing preventing you from doing it that way, it's not a good reason.
#1 should work, assuming you can find a school. And you are correct that it would be best not to leave the country until your wife made the switch to the trailing spouse extension (would not be switching to non-O, just changing reason for extension).
#2 would also work, but I would suggest not applying in New Zealand. The Thai embassy there charges about 5-10x the price for all visas as compared to other Thai embassies in the rest of the world.
Plenty of stick deodorant, but no Old Spice brand! And it's expensive to order from Shopee or Lazada. I always bring a lot when I come back from the US.