I still think we have two very different understandings of how Genjutsu works and what it does.

You're missing the point again. I already mentioned that it was not their chakra, it was Nagato's, they were controlled by his chakra, so working with given info all of the paths of pain should have been paralyzed as well, because they don't have their own chakra networks, so the only way to control them would be by controlling Nagato's chakra flow.

I don't even agree with this (assuming I understood it correctly). Let me try to dispel this belief. Firstly, we know Nagato sends chakra to the bodies, and that he receives chakra from the bodies as well in order to receive vision, sound, etc. This means there's a network of chakra, we both know that. However, he is likely able to closely control that network, in that he can choose what to send out and receive with precision. This is somewhat of an assumption but to provide an example, Nagato doesn't allow physical pain to be transmitted back to him. Otherwise when Kyuubi was smacking Tendo pain in the head with a giant rock, Nagato would have suffered some serious concussions. Another example, when Naruto got his sage chakra absorbed by the fat pain who turned into the frog, no one else got transformed even though we know chakra gets transferred to and from the pain bodies to Nagato.

This is why even though 3 of pain's bodies were caught in Jiraiya's sound genjutsu, none of the other bodies or Nagato were caught. The other bodies only heard the transmissions of the sound from the genjutsu, not the actual source of sound coming from the toads. I hope this was relevant to our discussion because it seems to be a basis for your argument.

I also see some issues with your bulletpoint arguments, but I'll leave them for now and see how you respond to the pain-genjutsu interaction first.

Ultimately I think you're still asserting a rule based on mere inferences (e.g. sharingan = eye powers = resistance to visual genjutsu only), even though there are rules that are specifically mentioned in the series that say otherwise. I'm trying to understand your side of the argument so have some patience.