I'll definitely keep this theory in mind.
Though I am not totally sure Naruto is a Senju, you've made some good points that may convert me with a little thought.
I am not sure he is a Senju because we don't know how many clans there were in the Sage of the Six Path's time. There weren't necessarily "clans", but people who learned his ways and separated into clans.
We haven't had any proof that the Sage is the first person to ever exist. We just know that he had the Rinnegan, laid the groundwork for modern ninjutsu, sealed the Jyuubi, and became the father/mother of the bijuu. If the Sage was the first person to ever exist, which contradicts what Jiraiya said about him telling people he was there to bring peace (which insinuates that there were more people around that time) then it may be more plausible that Naruto is a Senju because then everyone would be a direct descendant of his supposed sons.
It really depends on what you qualify as a "Senju".
If you have three Nara grandparents, then one from the Senju bloodline, is that a Senju? If that qualifies, then yes, most of Konoha, including Naruto, is from the Senju clan. If not, then that individual would be from the Nara clan.