I'm not petty enough to write off an entire franchise based on 10 minutes, even if it was the ending. I am happy with the story as a whole, even if it isn't perfect.
That being said, yes there are some things I would like to change:
ME1-
Remove this game's autodialogue. Let me explain: I mean, get rid of any dialogue wheels where every single option leads to the same exact line, or come up with different lines for each choice.
ME2- This is the game where most/all future problems stem from in my opinion since it does nothing for the trilogy aside from waste two years. As such, I would radically change it [sorry, TC, I am breaking your guidelines here, but I can't help it]
Make this game actually matter. None of the daddy issues, none of the "ah yes, Reapers" retcon, drop the Collectors plot we have. Replace the story with one where the galaxy is working on building up their militaries in preparation for the war, and the Collectors are not slaves to Harbinger. Instead, the Collectors are a race that, while using seemingly cruel and harsh methods, are out to stop the reapers too. They are working on a super-weapon that is capable of severely weakening the reapers to where they could be conventionally beaten. Their weapon runs the risk of killing millions of the galaxy's population because it would throw out a lot of radiation that would severely damage technology and people's DNA. [The collectors are okay with this because they are immune to its effects since they are advanced enough to have technology that could counteract it]. Of course, the galaxy doesn't know exactly what the collectors are doing, so everyone just assumes they are just being bad for the sake of being bad. By the end of the story, Shepard discovers the partially built super-weapon at the collector base. He would then have a choice to destroy the weapon so that they won't have to deal with its side effects, but setting the galaxy back in terms of preparing. Or he could keep the weapon, giving the galaxy a boost in terms of preparing, but leaving the galaxy with a need to try to find a way to counteract the effects of the weapon.
I would also make Cerberus do some very strange things at different points to better foreshadow their indoctrination thanks to TIM
ME3-
In this game, no forced of when to do Tuchanka and Rannoch. Instead, you would get to choose where to take the game first. Would you cure the genophage at the expense of a weaker Quarian/Geth, or stop the Geth/Quarian conflict at the expense of a weaker Krogan military? Should you go to Rannoch first, the Krogan will be weaker and thus, the Turian fleet will in turn be weaker. That would then cause a stronger Reaper presence on Earth itself because the Turian fleet would be less able to stop the reaper advance in the battle of Earth. Should you go to Tuchanka first, The Geth and Quarians would both be weaker, and because of them having more time to fight with each other, would be harder to make peace between the two. Since the Krogan are stronger, the Turian fleet will be stronger, and thus fighting on the ground on Earth would be easier thanks to the Turian fleet being able to slow the advance better. However, the Geth and Quarian fleets are weaker meaning more civilians will die because the Quarians wouldn't be able to assist evacuation as much.
Before I get into the plot, I will go ahead and say that Shepard is not locked up between the games, but still working as a SPECTRE. He doesn't lose access to his Normandy crew.
As for the plot itself, honestly, I am not quite sure how to write a war story, so I will just write details I would like to see used. After taking the crucible [as it is now named] from the collectors, Shepard has a good head start of preparing the galaxy. With the fleets built up, we get reports of Khar-shan [that is the Batarian Homeworld, right?] being hit with the blunt force of the Reapers. The council then green-lights the fleets to get ready for the war, sending them to various worlds. Shepard is given control of a second ship by the Council in addition to the Normandy SR-2 which the Alliance let Shepard keep after ME2. The Normandy is now the name referring to both ships, with one being named Omaha and the other named Juno. Shepard then splits the crews among the two ships [You choose where Miranda, Zaeed, Kasumi, Grunt, Samara/Morinth, Garrus, Tali, Mordin, Jacob, Jack, Virmire Survivor, Liara, Thane, and Legion will be. In the event where there is an odd number of squadmates, James Vega joins the ranks of the Normandy team].
Having 2 ships, Shepard can command both at the same time [when ashore, both ships are available to enter so you aren't stuck with going into just one of the ships]. And use one for meeting with race leaders such as Wrex and the Dalatrass. You can send one ship to take care of war asset quests that would replace the fetch quests while you can take the other ship with you on another side quest. At any time, you can call on members of one ship's crew if you are in the other ship and want to do a mission/assignment, but only if the other ship isn't busy with a War Asset quest, with said person [you would need to swap squadmates beforehand. With main missions, both ships are with you so you won't need to plan ahead of time who to bring. Joker pilots one with Chakwas as the Med-Bay person, while another pilot, I guess Steve Cortez, controls the other ship with Dr. Michel as its Med-Bay person.
Eventually, you would get word of something happening at Eden Prime, and if you go, you run into either James Vega, who would be a very talented soldier stationed there in charge of the other soldiers of Eden Prime sent there to fight off the inevitable reapers, or a replacement person doing the same thing. After doing your stuff there, and get Javik out of his popsicle, both he and James join your team [or just Javik if James was already in your team]. This would NOT be DLC.
As for Cerberus, I would keep them as indoctrinated. I was okay with them being that.
By the end of the war, once we get to earth, I would make it be a grander version of the Suicide Mission that actually uses the war assets. Instead of Destroy, Control, Synthesis, and Refuse at the ending, I would just have reapers defeated or reapers win. The way you played the trilogy in general, how well you did ME3, and how well you do in the final mission all determine how the galaxy fares against the reapers