I'm vaguely recalling what I had heard many years ago when I studied Nusach at the Belz School of Jewish music (part of Yeshiva University.)
Cantor Beer taught the course on Selichot and he was (and still is) a maven on Tefillah history. He explained that beginning at Tzaddik Hashem bechol Derachav is a "recurring" theme for Selichot as well as the High holiday season. One of the fundamentals of Teshuva is admitting the concept that "G-d is correct and righteous and mankind is sinful." There are similar phrases scattered throughout various Selichot and other Tefillot, esp. on Yom Kippur.
Similarly, the next verse, Karov Hashem Lechol Kor'av - "G-d is near to all those that call to him" - is likewise an appropriate Selichot / High Holiday theme. We pray and hope that G-d listens to our prayers and pleas at this time of year and forgives us for our sins and helps us perform better to serve Him.