Hiya, 
It seems you are much influenced by a particular interpretation of the suttas, and I think I can guess whose it is. Thatâs alright, of course. No problem. 
But for sake of discussion you may want to widen your reading a bit, because it isnât a very standard interpretation afaik. And therefore, to simply post a sutta and say itâs all very clear, wonât achieve much, because people will generally interpret it in a different way. Anyway, here are some thoughts:
No, bhavÄsava is the Äsava, not bhava itself. This word is a compound where the relationship between bhava and Äsava can be interpreted in various ways. Itâs not likely to be a kammadharaya, which is a technical way of saying it doesnât mean âbhava which is an Äsavaâ. More likely it means âthe Äsava for/towards bhavaâ, âthe defilement [aimed] towards existenceâ. On this, Sujato notes at MN4, âBhavÄsava is the defilement that craves to continue life in a new birth.â The continuance in a new birth is the bhava. Also:
This sutta too is generally interpreted differently. Ven. Bodhi notes at the similar AN3.76: âBhava. What is meant is a concrete state of individual existence in one of the three realms.â And he notes that this sutta describes âthe rebirth processâ. That is also how Sujato interprets it, as you can see in the translation you quoted: âThatâs how there is rebirth into a new state of existence in the future.â
The word for ânew state of existenceâ here is punabbhava, which means âa next bhavaâ, i.e., a new life. So this sutta doesnât âmake this relationship very clearâ. It only does so when you start reading it with a certain interpretation already. To me it makes no sense to talk about ârebirth into a new becomingâ.
The overall problem here is that bhava is never explicitly defined in the suttas. In that case we need to use context to determine itâs meaning. I havenât seen any definite indications for it to mean some momentary becoming and many that indicate it to mean a life. The Ratana Sutta says, for example, that the stream winner will not have a eighth bhava. This clearly means an eighth life, not an eight âsense of the futureâ or eighth âwondering about what will beâ.
Anyway, Iâm not sure what this still has to do with this viññÄáča anidassana. Were you aware that Ven. Sujato just posted a short essay on this topic?