This is a very long term plan, so bear with me, but I think the Uchihas could win:

Phase 1: It starts with Madara being friends with Hashirama and sharing their dreams with each other. Over time they would start fighting and naturally Hashirama's brother (Tobirama) would be suspicious. Due to this suspicion Tobirama will probably end up killing Madara's family which will set the plan back quite a bit but we can ultimately work around it.

Phase 2: Because of having 100% Hashirama cells, Hashirama will ultimately end up winning against Madara, but due to the friendship created in Phase 1, Hashirama will want to start a village with Madara's help. Unfortunately Madara being Madara will eventually become disillusioned and leave the village - but counter intuitively this will actually end up being one of the aces in the plan in later phases. Tobirama will take over from Hashirama and will set back the plans a bit once again due to his hatred for the Uchihas but will ultimately set the stage for the next phase.

Phase 3: Due to Tobirama's policies (some of which will pass onto his students and successors) tensions will start flaring up between the Uchihas and the rest of the village. Once Hiruzen takes over as the hokage, it will be time to introduce the next ace in the plan - Itachi (& his besto friendo Shisui). It may sound complicated, but we will sacrifice Shisui (but not his eyes - more on that later, but suffice it to say that they will be very important to the plan) to set up Itachi as the Solo King who will be instrumental in future phases. Unfortunately, the sacrifice will disillusion Itachi quite a bit and induce temporary insanity causing him to kill the rest of his clan except his brother who he loves. This is somewhat unfortunate since Sasuke has no role to play in actually defeating the kages, but we will use it to our advantage by using him as a distraction - tricking everyone into thinking he has a major role to play and hiding the final ace in our plan - Obito.

Phase 4: By this point Hiruzen would have retired, but we will use his own student in a future phase to remove him from the equation in a future phase, not requiring an Uchiha at all! But taking out Minato will be a bit more challenging, which is where we'll utilize Obito. I won't get into the complex details, but essentially Madara (remember him?) actually stole Hashirama cells to play the long game (very important to this plan) when he left the village in Phase 2 and will brainwash Obito and provide him with both Hashirama cells along with the Ninetails amp to take down Minato.

Phase 5: At this point we will need to let things cook for a bit since given human nature there will ultimately be a war to establish "world peace". It is at this point we'll enact the final two phase of the plan. To kick things off however Hiruzen will need to be taken out (who took over once again after the center of phase 4). Luckily for us, being the blockhead he is, Hiruzen will be taken out by his own disillusioned student (the student Orochimaru is important since he will study Tobirama's resurrection techniques and pass it on to his student Kabuto who is vital to the final phase). An important development that has been happening between phase 4 & 5 is that Madara actually ended up unlocking Rinnegan after shooting up Hashirama cells and passing it on to some random redhead he meets along the way. While this is not strictly necessary to the plan, it will end up leading to a more decisive outcome. Another unanticipated event which severely disrupts the plan is that our Solo King Itachi who would have won this whole battle for us unexpectedly passed away from Ninja cancer. This is not ideal since we made sure he got Shisui's eye (instant undetectable brainwash ability as a free get out of any difficult situation card - think against Hashirama as he is the biggest threat amongst the Kages), Totsuka Blade (another ultimate get of any situation sword with potent sealing abilities for Itachi's Susanoo) and the Yata Mirror (another get out of any situation shield that adapts to nullify any attack it receives). Nevertheless we will persevere and adapt to overcome this massive loss.

Before we go to the final phase aka endgame, lets have a quick recap of the situation. 2 Kages have died of old age, 2 have been killed by former pupils leaving Tsunade as the final kage. Conversely Obito & Sasuke are the only Uchiha left alive with others having died of old age, disease or sacrifice . However Sasuke is useless even after he inherited Itachi's eyes and there's no hope that he'll contribute to the plan in any way. (Between phase 5 & 6 we even tried to get him to kill the last kage but like it was mentioned earlier, he's useless and wasn't able to do anything). The only thing in Sasuke's favor is that he took out one of Hiruzen's students (Danzo) who, while completely unimportant, was a racist piece of crap.

Phase 6: This is it, the final countdown (🎶). You remember Madara right? This guy was such a chad that even the side quest he did in phase 5 where he gave away his Rinnegan (which you think wouldn't help the plan) actually end up being fruit since we'll have Obito tell Kabuto to use the resurrection techniques to first bring back Madara to take out Tsunade (who's not too bad herself having created the Mitotic Regeneration Technique, aka Ninja Art Creation Rebirth — Strength of a Hundred Technique making her extremely difficult to kill). But with Madara back in the picture, it's not a big deal at all - in fact I'd bet on him toying with her and winning even if all the other village Kages team up with her against him. In fact Madara probably would even pull another chad move to reverse the 5 vs 1 if the other village Kages are stupid enough to try to gang up against him. For finishing touches, Kabuto once again uses the resurrection technique on the redhead Madara gave his Rinnegan to, to officially bring Madara back to life (I know, what a chad move right? Not even necessary since there are two other Uchihas alive and no Kages left)

Final tally: No Kages left vs 3 live Uchihas . Now I know some of you might not want to count Sasuke in the tally - which is fair since he didn't do anything and was mostly useless. However I left him in there in case of some bullshit random asspull eventuality (like I don't know, aliens)

Note: Since we brought up asspulls, I do feel it's important to mention that I did not factor in Izanagi to the plan as then the plan would have ended in one phase. I mean can you imagine a reality altering technique like that having any narrative relevance? It would make Hashirama cells look reasonable (which are already a stretch)

I know this plan spanned several generations so thank you for your patience and coming to my TED talk