The final airline SHOULD allow her with the expired Thai passport, as she is returning home. You may need to use the USA passport before the last flight though.
There are luggage storage places in Bangkok. Also, if you work it right, you can stay at the same hotel near the beginning and end of your trip. They usually will store it for you. (Unless you are roaming Thailand for months...)
Thoughts? Sounds like fun when you say it, but when I start thinking about it, BKK to the border is probably at least 20 hours. Then you would HAVE to get off and do immigration stuff, then get on another train for 5 plus hours. Some people may enjoy that, but many wouldn't.
What I would do, as suggested by someone above, would be to catch several trains and overnight in a few Thailand towns/cities, etc. Then do the last slog in one go from the border to KUL.