just one thing, i only read your thread, not the comment so,,
i thought the 10t dont have rinnegan but that sharingan look alike red eye.
thats how i remember the very 1st time it was shown, no rinnegan,
so i think the so6p had the rinnegan. my point is...
obito managed to put sharingan and rinnegan to hid edo's
same thing with nagato's 6 paths of pain and summons, they all had rinnegan
so since obito is the one who summoned the incomplete 10 tails, i think he is the one who implanted rinnegan on it, and not sharingan because there is only one spot..
well, thats just my theory though,, just sharing. ill post this as a thread too =)