Thank you all - Kusala, Santa and Bhikkhu Pesala - for your responses.
All of you have directed me to the Discourse to Gotami amongst other texts. It's a perfectly good text, too, except that it doesn't help us decide "Why Theravada?", which is the basic question of the OP and the thread.
Why not? Well, as a text composed before schools differentiated, it naturally can't mention Theravada, Mahayana, etc. In fact, "The "authenticity" of the school is not the focus. It's the specific metrics on the results (which is measurable) that determines whether it's Dhamma or not Dhamma," as Santa said. Thanissaro said something very similar in the introduction to the texts Kusala pointed me to, and (fwiw) I agree entirely. The Buddha's guidance on this point is very pragmatic, as it so often is on others.
Here it could be modernised to, "If it works, it's good."
I think that's a great basis for moving forward in my practice - but it also justifies adopting any practice/s which "lead to dispassion, not to passion; to being unfettered, not to being fettered; to shedding, not to accumulating; to modesty, not to self-aggrandizement; to contentment, not to discontent; to seclusion, not to entanglement; to aroused persistence, not to laziness; to being unburdensome, not to being burdensome," whether they come from the Pali suttas, the Mahayana, the MBSR folk or, for that matter, the Kabbala. Equally, it throws the responsibility of discerning the difference between Dhamma and non-Dhamma upon me, while encouraging me to go to the wise for advice - as I do, but I will still always exame it critically, as I have done in this thread. Then again, the Buddha told me too.
I have just used "I" and "me" for convenience but of course what applies to me applies to everyone.