Spun off from what, and how?

I am not sure I can expalin that succintly at the moment. It is also hard to summarise how you get from counting apples to transfinite numbers.

Why does their being rational demand that they have values in common? Being rational means that they necessarily share a common process, namely rationality, but that process can be used to optimize many different, mutually contradictory things. Why should their values converge?

Rationality is not an automatic process, it is skill that has to be learnt and consciously applied. Individuals will only be rational if their values prompt them to. And rationality itself implies valuing certain things (lack of bias, non arbitrariness).

So what if a paperclipper arrives at "maximize group utility," and the only relevant member of the group which shares its conception of utility is itself, and its only basis for measuring utility is paperclips? The fact that it shares the principle of maximizing utility doesn't demand any overlap of end-goal with other utility maximizers.

Utilitarians want to maximise the utiity of their groups, not their own utility. They don;t have to believe the utlity of others is utilitous to them, they just need to feed facts about group utility into an aggregation function. And, using the same facts and same function, different utilitarians will converge. That's kind of the point.

But, as I've pointed out previously, intuitions are often unhelpful, or even actively misleading, with respect to locating the truth.

Compared to what? Remember, I am talking about foundational intuitions, the kind at the bottom of the stack. The empirical method of locating the truth rests on the intuition that the senses reveal a real external world. Which I share. But what proves it? That's the foundational issue.