I think if they done ME2 differently, get hints from Derelict Reaper or somewhere about Leviathans, have Leviathan quest in ME2, keep Harbinger in game but far more distant, have Arrival DLC kind of sequence in the Collector base instead of human Reaper and have your epic conversation with Harbinger there. So many ways to build it actually, but no... Cerberus and daddy issues. What exactly was wrong with Karpyshyn's much lower key Cerberus?
For ME3 thinking of various races strong / weak points and that because Prothean sabotage cycle was late, space faring races were more advanced than during previous cycles, I can see a way to get out of the corner and some of it happened, but what we practically got was the battle for Earth... that was like three relatively empty stages on Earth.
In my opinion, you can salvage the series quite well just by modifying the third game. ME2 was sub-optimal from a "setting up the conclusion" angle, but it did give us material to work with. Haestrom's sun dark energy subplot could have been used as a way for the Reapers to return (perhaps new mass relays are created by collapsing stars using dark energy stuff), or it could have been used as an insight that would help defeat the Reapers. Cerberus was working on gathering technology and weapons that could help end the Reaper threat in one way or another, they were studying the giant reaper killing gun that knocked out the Derelict Reaper in ME2, and they may or may not have access to the in-tact Collector base. The council races had access to technology salvaged from Sovereign at the end of ME1 - the "Thanix Gun" you get in ME2 as an upgrade for your ship is a Turian weapon reverse engineered from Sovereign's main gun, and more than doubles the firepower of an equivalent conventional mass driver weapon.
If you want to dig
really deep in the lore, there's a planet called "Rothla" that was accidentally shattered and turned into a debris field by a Krogan experiment centuries ago. There's the Leviathan of Dis (which was re-purposed for
Leviathan dlc) which could have done something for the main story. There was even like a Cerberus daily news thing once where they mentioned that the Batarians had set up some giant orbital solar laser grid or something (I can't find this anywhere, but I distinctly remember it from back in the day).
You talk about how this cycle's reaping is late, allowing the council species to tech up, and that's exactly how half of a victory should be explained. Not just have they had a chance to tech up naturally, they have access to Reaper corpses and other advanced precursor technology. They have advanced warning. The Relay network is still under their control because it nolonger responds to Reaper commands, meaning that the Milky Way's species can actually coordinate with each other, unlike previous cycles.
There's also another annoyance we can solve pretty easily. Why didn't the Reapers just fly back to the Milky Way hundreds of years ago when they first woke up? Apparently it only takes a few months, and there's no negative consequences. But what if there were? What if the Reapers
can't fly back to the Millky Way without major negative consequences, which is why they hesitated for so long? Drive cores need to be discharged as they build up huge quantities of electricity during their operation. In Dark Space, there's nowhere for them to do this. So imagine this instead - half of the Reapers need to shut down, and have their drive cores cannibalized by the remaining Reapers. This allows them to swap the drive cores halfway through the very long journey, and make it the whole way. The rest of the Reapers are still "alive", just in hibernation, but they are completely out of the fight until the Galaxy is pacified and the Citadel reconquered.
Since the Prothean sabotage blocked them, Shepard foiled their 2 shots of getting back into the Milky Way, they can now only bring half their force to bare. The Galaxy can coordinate in theory because the Mass Relays still work. They have access to more advanced technology. They have a few ideas for superweapons that might be able to help win a fight or two. It would be tough, but feasible to win, assuming the Galaxy can keep its shit together and work past their petty disputes.
It's not Shakespeare, but it's an "okish" plot that avoids star child crap, reliance on a never before referenced deus ex machina ("The Crucible") and references things established in the series for its resolution.