How we cite our quotes: (Line)
Quote #1
While this America settles in the mould of its vulgarity, heavily thickening to empire, (1)
Absolute power leads to vulgarity, which leads to an ever-thickening empire. They're all related to one another and that long narrative form helps us to visually link the pattern together. The "thickening" part looks to be pointing towards the idea of centralized absolute power where only the elite few have a say, as opposed to the republic America once was.
Quote #2
Out of the mother; and through the spring exultances, ripeness and decadence; and home to the mother. (4)
Mother Earth has the ultimate say over just about everything, since men, no matter how powerful they are, always end up back where they came from (earth). The cycle we see in this metaphor also relates to the cycles of power that grow and then decay over time just to be reborn in some other form. Even absolute power can't last forever.
Quote #3
But for my children, I would have them keep their distance from the thickening center;
corruption
Never has been compulsory, when the cities lie at the monster's feet there are left the mountains.
(7-8)
There's a choice folks: you can either be part of the thickening center of the empire and participate in the corruption, or you can get away from it and do something more positive for yourself. The decay is happening either way, but the speaker tells us that it's not mandatory that you actively partake in the corruption in order to get a piece of the power-pie. Eventually the powerful monster-empire will self-destruct and gobble those cities up, but hey, we can always climb a mountain instead.