On your first point, I'm not saying or even implying that his cliche speech was disingenuous. What I am saying is that there are many people in Skyrim who believe his words to be false.
Okay- I have no argument with that. Never claimed he was universally praised or not a controversial figure. Pick any political leader, especially during a time of upheaval, and you're not going to find uniform opinion on them.
Second, I rose the point of him not suppressing the songs and words of praise and his premature elevation to High King by friends and followers alike because you stated that he never wanted that title to begin with.
No, I said he doesn't think he has some divine right to it, just that
someone needs to step up and he's in a position to do something about what is happening in Skyrim. He expresses self doubt in a few of his dialogues (about leaving the Greybeards, for instance, or about being worthy of his father's seat), though that doesn't mean he's not ambitious or even arrogant. His battle taunts are delightfully arrogant.

He's just not the caricature of a power-mad, selfish egomaniac that the empire likes to paint him as. The reality is more nuanced.
For instance he also questions Galmar's idea that he should take the Jagged Crown because of its symbolic significance, though he goes along with it. I agree with Galmar- a certain amount of heroic aura is needed in poltiics. Why do you think the Medes wear the symbols of the Septim empire?
I think the idea that he should ban bards from singing about him kind of silly.
Third, one can never convince an entire populace to rebel on property rights alone. It is clear that what upsets the Nords most is the infringment on their culture and their worship of a person they consider a god being made illegal and punishable by even death in some cases. Ulfric takes up this cause. If he is not devout, he is insincere about one of the major reasons for leading the rebellion. And that ties back to what so many NPCs say about him.
His speeches never make devotion to Talos a central issue, rather that the Thalmor should not get to dictate who the Nords worship or don't worship. His bug is Nord sovereignty, not religious zealotry. I don't see any inconsistency here.