The Chronicler's psalter

I'd take some time over Psalm 135 and the Chronicler. Matthew Lynch proposes a division between Psalms 1-88 (+89?), and the rest. These are now Five Books; on the example of Torah, and maybe of 1 Enoch also. Chronicles is a brief for Reigns with the Psalter as soundtrack, the second part of that Psalter specifically. We're here enumerating according to the Masoretes, for simplicity.

1 Chronicles 16 might witness to Psalm 105-106 as the Davidic capstone of Psalter Book IV. Lynch argues that Psalm 135 was vital to Solomon's reign, in the Chronicler's perception. Psalm 135 had, for its part, borrowed not just from the obvious Psalm 136 but also from 115 and 134. Any student of Psalm 135 could have been aware of all four of these. Lynch argues that the Chronicler was, indeed, aware of all four and more: also Psalm 132, maybe of the 120-136 bracket which Jews term "The Psalms Of Ascent".

This, yes, stretches our evidence. Although: maybe not all that hard. If some readers of Books IV-V see a limitation to the respect due to Levites, which as Lynch points out obviously excepts Psalm 135; perhaps this is why Psalm 135 and the Chronicler came to exist, exactly to support those Levites against the murmuring of a fourth-century-BC demotic Jewry.