After a considerable time on the phone with LAN, we have now purchased our round-the-world tickets.
Something I learned: you do not need to take advantage of the "Canadian exception" in order to arbitrage the difference in round-the-world ticket prices. So long as you are willing to purchase an e-ticket (and none of the airlines that I spoke to were particularly enthusiastic or willing to issue paper tickets with open dates), it seems that an e-ticket purchased online through the OneWorld Alliance website will be priced at the cost of the country of origin. [1] Thus, it is often possible to save money by "starting" the trip in another country (in our case, Ecuador), and then booking a separate flight from the U.S. This is particularly true in our case, as the OneWorld Explorer is priced by the number of continents visited. Technically, we are not visiting North America on the "round the world" section of the trip.
If you are looking for more information on round-the-world travel, you could do a lot worse than signing up for the FlyerTalk bulletin boards, where there are a lot of very helpful and experienced travelers willing to answer questions from newbies.
[1] This may still be due to the "Canadian exception," as the booking agent listed on the online reservation is located in Vancouver.
Neat hack, I like it!