Peter wrote:I wonder... denial that rebirth occurs, or denial that the Buddha taught rebirth, or denial that the Buddha's teachings on rebirth are relevant to the Path... is that disenchantment or is it something else?
just the disenchantment of what SN 15 shows:
"Why is that? From an inconstruable beginning comes transmigration. A beginning point is not evident, though beings hindered by ignorance and fettered by craving are transmigrating & wandering on. Long have you thus experienced stress, experienced pain, experienced loss, swelling the cemeteries — enough to become disenchanted with all fabricated things, enough to become dispassionate, enough to be released."
by the way, in other translations the word "transmigration" is not used.
In this German translation in example, is "circulation of births"Warum das? Unbekannten Anfangs, ihr Bhikkhus, ist dieser Umlauf der Geburten; nicht kennt man einen ersten Beginn  bei den Wesen, die, in dem Hemmnis des Nichtwissens, in der Fessel des Durstes gefangen, (von Geburt zu Geburt) umherwandern und umherlaufen.
 P. pubbā koti, bezieht sich nach dem Komm. II. 197.16 ebenso wohl auf den Anfang wie auf das nicht abzusehende Ende.
if somebody here is expert in Pali language, maybe he can explain the exact meaning of the pali word involved.
Anyway, I think one must be aware of the implicit dangers in using the word "transmigration" due the inoculated term "migration". Because there are many types of multiple birth, not only transmigration. We have metempsychosis, transmigration, reincarnation, rebirth, recorporation, metemsomatosis or palingenesy. Among many others.
You must ask the Western translators why they are using this word instead another one. On my side, I think much closer to Buddhist doctrine the use of another words like Palingenesy: http://thinkexist.com/dictionary/meaning/palingenesy/
# (n.) That form of evolution in which the truly ancestral characters conserved by heredity are reproduced in development; original simple descent; -- distinguished from kenogenesis. Sometimes, in zoology, the abrupt metamorphosis of insects, crustaceans, etc.
# (n.) A new birth; a re-creation; a regeneration; a continued existence in different manner or form.
an important discussion can be the right use of the words "transmigration" or "rebirth" beyond the denial of a causal thread in the arise of beings. I think the causal thread is out of doubt inside the Buddhist doctrine. But this confussion of the Buddhist rebirth with a transmigration it can start in the bad choosing of translated words. Or perhaps unavoidable?
It can be an interesting topic to clarify with the people expert in Pali language (not me).
Anyway, I'm referring to the Buddhist rebirth of those passages involving other lifes, and used like support to explain other things like sila, craving, etc... Regarding those teaching of Budda which are directly referred to the Rebirth and its cease, all them are teachings for the present moment, here and now.