I think you're a little fixated on the word "rebirth". I'll admit, it's not the greatest word. It's better than "reincarnation" (lit: enveloped in flesh) but it still sounds like it's got too much "re" going on. You seem well aware that there's nothing to "re", so good for you... you recognise that one moments conditions the next, which conditions the next. Sweet. All totally in accord with the suttas.
The only way you threaten to deviate from the suttas is if you do not recognise that the process of one moment conditioning the next, and the next, and the next.... does not stop
simply because of conventional death. It depends on if you think all mentation is "snuffed out" at conventional death and thereby refute that actions can have consequences that span beyond so called "death".
"Do not force others, including children, by any means whatsoever, to adopt your views, whether by authority, threat, money, propaganda, or even education." - Ven. Thich Nhat Hanh
"The uprooting of identity is seen by the noble ones as pleasurable; but this contradicts what the whole world sees." (Snp 3.12)
"To argue with a person who has renounced the use of reason is like administering medicine to the dead" - Thomas Paine