End of one book and the beginning of another

Psalm 41, 42, and maybe 43: One of the issues (problems? challenges?) of my chronological reading of the Psalms at the pace of two a day is the shape of the Psalms doesn't necessarily lend itself to my schedule. Psalm 41 is the end of the first of five books of the Psalms, and the lament in Psalm 42 carries over into 43. So I could just read Psalm 41 today and catch up with three chapters tomorrow, or I could read both 42 and 43 today and have more material to deal with now. Or I could stick to my two chapters and not read Psalm 42-43 the way it was intended to be read. Read on for my decision....
In my reading of Holliday's The Psalms through Three Thousand Years for another assignment, he discusses when the Psalms were ordered and shaped into what is known as the Psalter, probably in the 3rd century BCE. Before that, psalms continued to be written or adapted and collected from other traditions. There's way more to this story, but for today's purposes, I want to point out a few things:
Psalm 41 ends with a doxology, which signals the end of the first book:
"Blessed be the LORD, the God of Israel, from everlasting to everlasting. Amen and Amen." (13.) Holliday says this general benediction isn't connected in any way to what went before it in the psalm.
Psalm 42 has a superscription to the leader, a maskil of the Korahites (which means sons of Korah). Holliday says this psalm is from the Elohistic collection.
Psalm 43 has obvious literary connections to 42. Both Psalms end with the same refrain: "Why are you cast down, O my soul, and why are you disquieted within me? Hope in God; for I shall again praise him, my help and my God."
And I really wanted to discuss some of the lovely imagery in the beginning of Psalm 42, which many of us know from various hymn traditions. My classmates will have to wait until my presentation on Thursday.