You're right about the transmigrants part, it completely slipped my mind that Hashirama wasn't the transmigrant at that time. One thing I'm not willing to accept is that Naruto and Sasuke don't have the Rikudou chakra any longer. That would mean that Sasuke has enough chakra on his own to enter Kaguya's dimensions and still have enough left to use his Sharingan and Rinnegan, despite BZ emphasizing how chakra-taxing dimension jumping is, which I'm having difficulty believing. Also, Naruto's RSM is more like a result from Hagoromo's Yang half + 9 Biju Chakra mixed into his BSM, which resulted in his Six Paths Senjutsu Mode. Since I don't believe either him or Sasuke lost Rikudou's chakra, Hagoromo confirmed Naruto is a meeting place between the Biju and he obviously still has his BSM, he should be able to manifest RSM normally.
I never said that Naruto and Sasuke don't have Sage Chakra. I simply stated that if the chakra is gone from from their bodies, then, at least Sasuke wouldn't lose Rinnegan. The mutation has already happened. Just like, for example, Kakashi's Sharingan mutated because of Obito. A sharingan cannot mutate without the release of a special Uchiha chakra within the head. But the mutation had happened, and the eye had already changed. It was not going to revert back just because Kakashi didn't release Uchiha chakra into his brain.
Second we have Nagato's example. Madara was the one who experience the mutation in his eyes. But the eyes had already mutated. Even when they were parted from the original chakra source - whether it was inside his brain or body - the eyes still remained Rinnegan and Nagato kept using them. This is the best way I can explain it.
With Sasuke, I agree. Even with Hogoromo's chakra, he shouldn't be able to shift dimensions. As 1) it's half the chakra and 2) the technique is too taxing even for Kaguya whose chakra far exceeds Hogoromo's full reserves. But, he is able to. Why? Because 1) his Chakra Control is at the Sage's level, and we know from part one that the more the CC, the less chakra is used and viceversa. 2) His chakra is extremely powerful and he can manage far more with less. We have known this from the start. 3) He already had a similar technique and got better.
These three factors make up for the large chakra. That is the only logical explanation.
That is slightly wrong. Naruto, for one, cannot use two Sage Modes at the same time, so it certainly isn't a combo of BSM and Sage of the Six Paths mode, which is RSM. When he kicked the orb, he was using RSM. He was given Senjutsu chakra from the sage, which results in "Sage of the Six Path Mode". This, combined with the chunks of chakra from all Bijuus results in that black and yellow cloak and TSBs. It isn't an RSM cloak. If you recall, Obito immediately gained a TSB when he pulled out Senjutsu chakra and Bijuu chakra from Madara's body. This Senjutsu also allowed Kakashi to use that ill-fated PS.
I don't believe both of them have lost Sage's Chakra. It seems less possible for Sasuke, to be honest. The meeting place has nothing to do with Sage Chakra, it's just Ninshuu; something Naruto did well before he even combined his Chakra with his Frog Sage Mode. My two cents.