Since you requested for something insightful, it might drag on from my end as well. This would have to do with certain inconsistencies and possible loop-holes in the manga which can be exploited for different factors. I will begin by suggesting that you actually took time with the analysis, so that in itself is quite commendable, my friend. I have disagreements, henceforth, I hope you do not hold it against me.
First is the trouble with the God Tree granting chakra. Either everything is lost in translation or something went wrong with Kishimoto, then it was a established fact from the start - and was repeated through out the course of the manga - that Chakra is a fusion or combination if Physical and Spiritual energy. Now unless people were devoid of Spirit altogether, then one can believe that the Sage somehow began the line that would carry it, making it seem that he would be the first human or Adam - the allegory of Ambrosia just cannot be overlooked.
I will add something from my post on another forum:
The whole tree and knowledge debate is very odd given the inconsistent flip-flopping nature of its author.. At first, it was set in stone that Uchiha and Senju were the thinned blood lines from the older and younger sons, hence the only people explicitly connected to the sage. This is backed by the development of EMS into Rinnegan; as Madara explicity explains that both Senju and Uchiha Dna are required to make the whole or make the two forks or blood-lines whole again. Furthermore, the Sage was the first person to give the knowledge of Ninjutsu. Now if one is to consider the other two factors, it's obvious that the spiritual energy or Chakra was there but the means to harness its power were not.
Put the God Tree into equation and it probably - my best guess, given the mentioned information - acted as a catalyst or even became a source of knowledge as in the Christian and Islamic Mythos. Now once I combine all of the missing pieces, I become hard-pressed to not brush aside the obvious tear in the theory in regards to the Sage being the sole father or Adam for all the blood-lines. It completely goes against the established factors.
Naruto may unlock the Rinnegan as you suggested, but, if the author clings to a thing called Logic, it seems quite the impossibility to me. So far most people supporting the Sage being an Uzumaki himself will have to reconcile with the idea that this Blood-line simply branched off from the Senju Clan - the thinned line of the younger son, as explained by Obito. Albeit Naruto is called an Uzumaki, he doesn't share a pure blood-line, whereas Sasuke does and so did Madara because of Clan in-breeding. Uchiha Clan is one of the most pure lines in the entire manga.
If you consider these factors, it seems more logical - despite the fact that I am not all too thrilled for it - for Sasuke to go beyond the barriers of Eternal Mangaeko Sharingan to Rinnegan rather than Naruto, who not only has nothing in common with the aforementioned blood-lines but is an impure Uzumaki. He might have been called by his father Clan, as he's what you would called a hybrid child as far as blood-lines go. So does that put all of the previous tablet talk? Your guess is as good as mine. And for Naruto to unlock the Rinnegan; I for one would find the elaborate liberties to be just as distasteful as others such as Minato's varied modes for starters. This one is a dead end for me, given the large and glaring evidence from the not-so-distant chapters. It would be like ignoring the elephant in the room.
Then is the case with Sasuke. Kamui - if you recall Obito's chapter Alive, I believe that is what it was called - was present when Obito still had 2 Tomoes as - if memory serves me correctly - Madara explicitly comments that Obito survived from getting completely crushed as he 'somehow seemed to slip away' from the boulder. We are all fully aware that Obito's Kamui is two-fold and yet, it's the same technique. He simply teleports his body that comes in contact with any attack in lieu of objects.
Now this could be a good indication of time manipulation based on 'Necessity', as he was about to be crushed to death, hence the desire in his mind to Slip or Elude Fates. This is interesting, as the brain's thought patterns trigger the Sharingan Mutation in the first place. I have a theory as to why Itachi's MS or Moon eye which is Tsukuyomi is more developed than most Uchihas and yet, still at a lesser tier than Shisui's. It's because of Uchiha scrolls he deciphered or read along with tablets when he was young. This was explained through Sasuke's conversation with Hizuren. Shisui already had developed MS and had excess to the tablet and could decipher more. I am adamant in my beliefs that it's the tablet that triggers the Doujutsus to develop in certain manners.
Madara wanted to protect his clan, hence Perfect Susano'o was acquired quickly during his prime, Sasuke wanted revenge, hence variants of Sun eye or flames of hell, Itachi deceived and lied just like Shisui - both worked as double agents - hence Moon or Illusions. Obtio's eye reacted to save his life, hence the notion to 'slip through or away from fate'. I doubt he had read the tablet as he was killed on the battle-field when he awoke the Sharingan the first time, but the other evidence is quite suitable as to how the eye itself reacts to the individual wielding it and how the tablet escalates the process.
Given the evidence, Obito only had the ability to 'Slip through or away' but by seeing the contents of the Tablets through Madara's Genjutsu, he was able to fully develop the ability to teleport others effectively. Then is the issue of MS's development into EMS. Recall the chapter where itachi tells the tale of attaining Eternal Light. It shows a statue of EMS with four eye sockets. It shows three Tomoe Sharingans but those are 'Clear' metaphors, as all MS have different patterns bar Obito and kakashi's as, let's face it, those are Obito's eyes. This would mean that EMS is developed through fusion of two MS pairs and this would ultimately translate into Sasuke possessing the power of his own and his brother's eyes.
I am very certain that that image you posted of Sasuke doesn't take the 'flow of power' in a literal sense, but it's a very common metaphor and more so, in regards to eyes that lose their light and attain in eternally through taking another ones as well. This is further backed by the fact that many Uchihas had MS and yet Sasuke is the second person to unlock EMS, which would mean that when the eyes still have a bit of light, they are harnessed by another to regain the ultimate form of Sharingan. And that would be an impossibility, as no one would be ready to relinquish their eyes. If what you suggest - and others - is possible then Madara won't be the only one to attain EMS before Sasuke.
Now coming back to the main point, then yes, Itachi specified that there would be a new doujutsu once one acquires EMS. Now what alterations did the tablet made within Sasuke? Was it to rectify history future in regards to the political setup? I think given his latest leanings, I suggest that he wants to change the fate of the future by breaking free of the illusion that would manipulate 'Time'. So yes, I do agree - and I have made this point myself as well on many occasions - that Sasuke would attain Yomi as you put it or a new Time Manipulation technique.
Great Read. I cannot rep you as I need to spread it around first, but a thanks is in order. If I can manage it, as most forum functions do not even work for me. I apologize beforehand if you don't see thanks from me under the said tab. Great Job. Also, I hope I didn't drag this along to long. Lol