Carnegie's How to Make Friends and Influence People has a slightly parallel approach: reread the book on a regular schedule, as you'll notice things the fourth time you didn't notice the third because your skill growth puts you in a different place relative to the material. (Maybe he also recommends not to read the whole book at once, also, and I just forgot that part; I think he does encourage people to read just the parts they want to.)

It seems to me that rereading is likely to be more effective than staggering the reading, and that rereading enables staggering. One of my childhood English teachers was more forgiving of reading in class than other teachers, and had a small rack of books available- one of them was Watership Down, which I read cover to cover probably ~7 times, and afterwards would just open to a random page and then would be able to immediately place myself in the story at that point and read from there.

This also calls to mind the practice among more serious Christians of reading the Bible once a year- it takes about four pages a day, and does not take many years for much of it to be very familiar. Muslims have the term "Hafiz" for someone who has memorized the Quran, which typically takes several years of focused effort, and I don't think Christians have a comparable term, but I've definitely noticed phrases along the lines of "quote chapter and verse" for when people had sizeable blocks of the Bible memorized.