The above seems incorrect. It seems the Buddha was not bound to the sensual bhava because it seems sensual bhava is a state of mind.
Also, I have never read the term “sensual realm” (“kamaloka”) in the EBTs. Possibly you could offer a quote for me. I have already read about human, godly, ghost, animal & hell realm.
Note: This matter is unrelated to denial of “rebirth”. “Jati” is there to accommodate ‘rebirth’; as has been held for 100s of years by Buddhists. For example, it seems explicitly clear in DN 15 that the various human, godly, animal realms, etc, are included in “jati”.
Again, the above seems contrary to Dhamma principles. These ideas seem to completely ignore the transcendent (lokuttara) state of Noble Ones.
“Bhava” obviously does not mean a “lifetime existence”. The suttas refer to “bhava” as an “asava”. An “asava” is a mental defilement.
It seems to not be “some” translations but merely one translation. AN 3.67 does not seem to refer to “rebirth”.
The word “abhinibbati” seems to simply means “production”, as found in MN 93 about “producing” heat from fire. Thus, in the context of AN 3.67, new becoming is “produced”. In the context of SN 12.2, new jati is “produced”. “Abhinibbati” seems to be neither a synonym for “bhava” or “jati”; just as “bhava” seems not a synonym for “jati”.
To conclude, again, your ideas may lead to a sabotaging of Dhamma practice. “Bhava” seems to mean “mental becoming” or “mental existence”, regardless of whether a Buddhist believes in rebirth or not. It is the state of mental becoming that determines the “jati” of human, godly, ghost, animal or hell. If practitioners ignore bhava; ignoring what states their mind are commonly or predominantly “established” in, then it seems they won’t be above to determine their future state.