EsquireSandwich

Given that P&T's solution was wrong this is possible but I think that their solution makes a lot of sense as well.

There's only 250 or so pages in the book and whenever she picked a page it was not the standard-you pick the page, the line, and the word number and I tell you the word. Instead, she just picked the page number and he said (on that page there are X paragraphs and the 2nd one says this). So he doesn't have to memorize the whole book, just something for each page.

Then if there is some sort of code to help you work it out based on the page numbers, you could legitimately memorize the 250 different pages. So the page number would be a clue to you of how many paragraphs, which one you're looking at, and maybe a letter to help you recall the word or phrase to recite.

This is a plausible method of doing the trick, with lots of practice and memorization.

Did you really just finish that last cube in time or were you trying to time it so you finished it at the buzzer?

you've been lucky. Having done a few escape rooms in NJ, many will put multiple groups together.