Pretty sure I stated that no progress is made regarding the "overarching narrative" of the entire trilogy. I.e. The Reapers and finding a way to stop them from doing what they've been doing for millions of years. And in regards to that specifically, it's a fact that none was made in ME2.
Containing the entire beginning/middle/end of a galactic war whilst beginning the search and finding of a solution to it and learning the main villains motivations is waaay more to ask from a single game than what ME1 did. ME1 introduced us to a fictional universe and started us on a quest that had us stumble upon something way bigger and said "to be continued".
Sure, in ME2 they flesh out the universe and we get to meet fairly interesting characters by galavanting all across the galaxy in order to help them with their mommy/daddy issues, only to conclude with the destruction of a single base. That means nothing in the grand scheme of things. They could've fleshed out the MEU whilst keeping the onus on what the first game started.
Introducing the Collectors out of the nowhere and basing an entire main plot of a game around them was far more wasteful than having Cerberus turn out to be the extremist splinter cell they always seemed be from the beginning by the time ME3 rolls around. Maybe if you were never forced to join Cerberus and spend a whole game being spoonfed how edgy and cool they are, Bioware wouldn't have had to shoehorn their real identity and motivations into the third game, just as they did with the entire Reaper plot.
Saving the entire Reaper plot (invasion,war,explaination of motivation/search for solution/resolution) was as big as a mistake as saving the conclusion to the Clone Wars/ Anakin Skywalker's seduction and fall to the Dark side and transformation/fall of the Jedi Order and the Republic/Rise of the Empire and Darth Vader/Birth of Luke and Leia into a single movie. It's a ridiculously overblown task due to it's predecessor spinning its tires.
As I said, ME2 is a fantastic game standing on its own. As the middle installment of a trilogy it is extremely problematic. Remember ME1? At the end when Shepard walks away from the Council after stating that The Reapers are out there, they're coming and "I'm going to find a way to stop them." He should've added: "as soon as ME2 is finished".
And that's what no progress looks like. That thread isn't even picked up until the Reapers get here. It's ridiculous. Can't excuse the complete absence of focus on the overarching narrative in order to simply introduce us to some new characters and flesh out the game world. Both of those could've easily been done. Killing off Shepard only to bring him back to work with Cerberus to fight a newly introduced enemy out of left field, and preparing for that fight by being said new characters space therapist, was a gross convolution of the central narrative. In fact, none of it had anything to do with it. The whole second game goes on a complete tangent. It's a glorified side story. Literally a spin off. That's not what the middle installment of trilogy is meant for.
While ME1's stakes were most certainly smaller, it had the exact narrative structure ME3 should have had: a recurring antagonist that gets progressively developed, exploring smaller narrative arcs on planets while searching for something to stop the antagonist, and finally a race to defeat the antagonist.
I think you're making the problem vastly bigger than it need to be:
-Invasion is merely the beginning of the story. I don't know why you think this needs to be a complicated plot point. Reapers come in and start killing. Done.
-War is progressed simply by doing missions. It doesn't need to be some protracted campaign like the previous cycles; you're Shepard, the protagonist, and it's your job to end the war quickly.
-Explanation of motivation could be achieved by actually talking to the Reapers. Had BioWare not thrown Harbinger's character out the window or actually given us useful snippets of information from our talks with Reapers, maybe ME3 would have been better. There were plenty of times, beginning, middle, and end, where BioWare could have developed an explanation for the Reapers. They just didn't.
-Search for solution could happen while talking with the Reapers as well. As you defeat more Reapers and solve each race's problem, you gain more information about how to kill them. Maybe they have a kill switch somewhere. Maybe killing Harbinger kills them all, because they're a hive mind or something. My point is that the solution can naturally emerge from the antagonist itself.
-Resolution would work exactly like ME1: a big friggin' battle.
So yes, ME3 could work almost exactly like ME1. Sure, it would have bigger gasps, bigger guns, and bigger drama, but it would still be the same story arc in essence.
ME2 might not have given the perfect foundation for ME3, but don't tell me it caused all of its problems. ME3 could have easily been a solid game. It just wasn't.