Although cradle Orthodox, I was brought up by my Protestant mother (not a believer, but ardently pro-Protestant), and I basically grew up with a lot of Protestant theological ideas without knowing it. (Side note: the old edition of the OSB ironically fueled this.) As a result, I complained in middle school that Catholics pray to saints. (Our church did everything in Greek, so I didn't understand anything.) I have thus always been uncomfortable with prayers to saints, especially when I began to read the "real" Orthodox prayers out of books.
I've prayed the post-Communion canon in the OP, I beg the Mother of God to "save us/me," and I "place all my hope" in her. I also feel deeply offended when anybody says the slightest irreverent thing about her. How do I understand these prayers?
I think the theological ways that people try to explain away these verses by claiming that they don't mean what they say are off-base. On the one hand, all Eastern hymns, prayers, and even stories about saints are bursting with hyperbole. The Apostles' sound did not go forth into all the earth, nor did their words reach the end of the world. It's a truth told in hyperbole. At the same time, it's still profoundly true. Same thing with the prayers to the Mother of God: hyperbole, yet profoundly true in a way we should never downplay.