Your alternative hardly changes anything. Without Reaper tech jammed into their code, the quarians fry the geth as soon as totally not Reaper controlled or green Borg drone assimilated Xen and Gerrel realize what has happened, just like they were about to over Rannoch (unless you slaughtered their entire species just to get at them, which I doubt you did with your insistence on happy endings). EDI without Reaper tech isn't even the same AI. At best, it's that murderous Hannibal system that caused the Luna incident, and more likely it's just rendered nonfunctional with intergral parts of software making up its OS deleted. Either way, it's for all intents and purposes just as "dead" as in the current Destroy ending.
If neither of those things happened, then you are basically taking parts of Synthesis's transhuman mind controlling, robot sentience applying space magic, so why wouldn't you just pick synthesis anyway?
In regards to EDI, I don't really care about after-the-fact word of god tweets and similar BS, but I do want to point out a few things:
A. The words "Reaper Tech" are a phrase used to describe... something. We don't know if it's software, hardware, or blood-magic.
So when we say that "Reaper Tech" got destroyed, we don't really know what was destroyed precisely.
B. Because of the nebulous nature of the term "Reaper Tech", I don't think we can assume that EDI was transformed into a different and potentially hostile AI (or even destroyed), because while I believe that "Reaper Tech" was used in the creation of the mobile platform and some of the Cyber Warfare assets, the AI itself is likely similar if not identical to traditional AI designs.
C. Regarding the Murderous AI on Luna, we don't really know what happened there, it could be and even likely that Cerberus took the short and stupid route like always, and pushed some button that they shouldn't have, so that they can measure the effectiveness of a weaponized AI and what it actually takes to dispose of it.
EDI itself, which is an evolution of said AI, was proven as an entity willing to cooperate and exist side by side with organics. Despite my misgivings about AI in general and the totality of their danger (the potential danger is actually on the level of what Dr Archer said about his "AI" - a technological apocalypse), I believe that such an entity deserves to be given the chance to exist, if only because we need to understand why some AI become homicidal and others don't. AI has a great positive potential as well, and learning how to minimize risks by working with an allied AI seems to me something of the highest priority.