The whole theory and explanation is great and i do agree with you! This thread is great!
But what i dont completely understand is where you say that the rinnegan comes about through the juubi. Madara and Obito both awaken the rinnegan without every coming into contact with it, let alone becoming its jinchuurichi
Its stated that to get the rinnegan you need the body of a senju and the eyes of an uchiha, not just uchiha dna although it could be argued that by having uchiha dna that you basically do have the sharingan.
If what youre saying is true, and the uzumaki bloodline is what the senju and uchiha bloodlines are derived from, doesnt that mean that the uzumaki possess the dna of the uchiha and thus the ability to awaken the sharigan?
Nagato, being of uzumaki lineage, has the senju body part of the rinnegan down, and through Madara's eyes being implanted in him, he gains the other requirement to awaken the rinnegan, which he succeeds in doing.
However, and this is only my highly unlikely idle speculation, but i think that the so6p was indeed uzumaki and that he had his children with a hyuuga woman (this adds a link to with the current storyline ie naruhina as well as the fact that rarely brought up fact that the sharingan is a mutation of the byakugan).
I'm still trying to compensate for the fact the sage is always depicted to have rinnegan with the inferrence that he used his occular prowess and sealing techniques to become its jinchuurichi. Its so very extreme but maybe the sage's wife gave him her byakugan, or more advanced byakugam (which ive seen mentioned in a couple threads but i still dont know what it is), thus combining with his already strong uzumaki body to awaken the rinnegan with which he uses to become the juubi jinchuurichi.
In terms of the distribution of power i agree that the very powerful sealing techniques would have only been shared with the same bloodline as him (wanted to say same clan but yeah), and that the physical attributes that are attained from parents in children would be continued, with his strong uzumaki body manifesting in the senju (possibly have stronger bodies and more stamina than uzumaki's as seen by Hashirama "rousing" his chakra and making a room come apart, something that naruto, of uzumaki blood is not once seen doing. in my opinion it could be that the physical strength of the juubi in combination with the body of the uzumaki is what creates this power) and his occular prowess manifesting in the uchiha, with the origin of the sharingan being the same as what you stated in your OP. Initially, the swirl pattern originally coming from the interaction of juubi eye chakra with his mothers byakugan, By having their mother as a hyuuga, i allow the statement that the sharingan is a mutation of the byakugan to become true. Ie, the swirl pattern is a combination of the juubi's eye and its chakra with the byakugan that mutates to form the sharingan when strong feelings of hatred are fostered.
This is the very brief course of events that i think happened
So6p Gets wifes eyes>gets juubi>has kids>nearing the end of lifespan split juubi into bijuu. Compensates for the fact he has white hair whenever hes depicted, probably he had characteristically red hair of the uzumaki which turned white upon massive exertion, for example splitting the juubi into bijuu, similar to how Nagato's hair turns white after resurrected a bunch of leaf villagers.
This does seem weird to me because he would have had to do her when she didnt have eyes which seems weird but its fiction so whatever, anything to progress the plot.
Tell me if you think theres anything ive missed or if theres any flaws in my logic

Thoroughly enjoyed your OP mate