Shamus, I think your analysis of this is deeply flawed because it considers some fringe components to be serious "sides" of the discussion and omits perhaps the most important part of this entire thing:
The most important part of the ME3 fiasco is that Bioware made specific promises about the ending of the game and what it would include. Bioware made it clear with direct statements that Mass Effect 3 would both answer all the outstanding questions and would NOT include a simple "choose A B or C ending". Bioware proceeded to put in a "choose A B or C" ending anyway, what's more many of the biggest questions in the series were not answered. Bioware released an app that was "behind the scenes" of ME3 and in that app they had the devs saying "well, we decided not to answer a lot of the big questions because they work better as mysteries and give us material for later games in the franchise". Add to this some leaked information about how Bioware actually had no plans for the ending until late in the process, and how what they did was inspired by an adolescent fan whose fan-letter got taped to a director's door, and you can see why there was a riot.
It should also be noted that changing the game genera in this case is a little different than your presenting it. Mass Effect (the original) worked as a self-contained story. It was also a game in a very niche genera as you pointed out. The problem isn't so much that Bioware decided to make a sci-fi shooter, but that they made it "Mass Effect 2" basically claiming that an entirely different kind of game, with entirely different core principles (as you pointed out) was "more of the same" following the first game. Basically Bioware should have created an entirely new franchise for that, and left a game a lot of people fell in love with alone rather than ruining it by stamping a "2" on something entirely different and then claiming anyone who complained about this was being unfair.
When it comes to that transition, also consider that it's not really fair or accurate to say that the first "Mass Effect" as any kind of an underperformer, or that it's criticisms by the shoot-bro crowd were especially relevant. After all it succeeded well enough where they wanted the franchise name for other games. It could have succeeded just fine where it was even by AAA standards but basically EA/Bioware wanted more money, and figured it could piggyback off of the success of the first game by using a title people loved, while otherwise making an entirely separate kind of game and using some of the same story elements and lore. This did indeed move more units, but it also meant that all those people who came to the game because of the first one felt rightfully betrayed, as they were being exploited, probably to form a "safe" foundation if for whatever reason they didn't draw in a whole new market.
The same can also be said about "Dragon Age 2" to an extent, which also pours fuel onto this fire. A game that was specifically created and hyped as a series acting as "the spiritual successor to Baldur's Gate" and using similar sensibilities was turned into a brawler. Not just a brawler, but a lazy one, where you see loading screens suggesting tactics conceived back when the game was still going to be a real RPG (like suggesting having fighters block for mages in a party formation).
I'll also say that I don't think the ending of "Mass Effect 3" went over anyone's head. The problem with the ending is that it didn't fit with the rest of the series, which even in the first game involved a hero who pretty much resolves no-win scenarios. Furthermore the whole organic vs. technological argument and the "inevitability of conflict" makes no sense if you subverted the whole logic by say bringing peace between the Geth and their creators... or even just sided with The Geth for that matter.
The actual reason for the ending is pretty much to level the universe, so they have a blank slate for franchise potential. Basically with the way they ended things with exploding gates and the like they can argue that anything survived or didn't survive, and feel free to pretty much ignore the entire trilogy in moving forward with the franchise... which was the bottom line because a series intended to end as a trilogy at most got turned into a franchise by corporate suits who insist on milking anything and everything dry. The ending is crap for fans, but pretty much perfect for developers who want a relatively blank slate to work from.
Rather than a lot of separate voices "talking over each others heads" there are disagreements, but pretty much everyone agrees that the ending was garbage, and that Bioware should create a new one, more in keeping with the spirit of the series. Not to mention that any such ending needs to be done so it is not simple a "choose A, B, or C" option because Bioware promised it wouldn't be one. What's more any such ending and the events leading up to it, should resolve a lot of the bigger questions leading up to that. If Bioware wants to do more "Mass Effect" after achieving that, more power to them, but the whole "Line" is united in the stance that Bioware needs to keep it's promises in regards to the trilogy and give the story of Shepard a proper ending fitting the character and the spirit in which it has been operating.