While guessing that there is more than trivia and coincidence in such an unusual arrangement of songs, I think I see additional irony.
As Steve of WV pointed out in a response to the last post, the shortest Psalm is expansive in its invitation for all nations to celebrate the mercy and truth of the Lord which lasts forever.
By contrast, the longest Psalm has about it a certain constrictive effect that is as humbling as it is personal. After 176 verses of celebrating the law of God, the song writer says, “I have strayed like a lost sheep. Seek your servant, for I have not forgotten your commands.” (Psa 119:176)
In between these two songs there is a middle song that alludes to the story of the nation of Israel (Psa 118:1-4) and the personal story of her king (Psa 118:5-21). Both in turn are part of the greater story of the One who, through his rejection and suffering (Psa 118:22-23), has made it possible for people of all nations to celebrate the eternal mercy of God (Psa 118:1; Psa 118:29).
It is that day of rescue (a future day of crucifixion and resurrection) that was in view as David declares “This is the day that the Lord has made. We will rejoice and be glad in it” (Psa 118:24)….“Oh give thanks to the Lord for he is good, for his mercy endures forever” (Psa 118:29).
So is there an intended relationship between Psalm 118 and the longest and shortest songs/chapters in the Bible? I think so. But what I’m more sure of is that all three ultimately support the story that is fulfilled in Jesus’ life, death, and resurrection. It is because of his mediation that people of all nations (Psalm 117:1-2) can be invited to celebrate the mercy that is needed by every one of us who says, ““I have strayed like a lost sheep. Seek your servant, for I have not forgotten your commands.” (Psa 119:176)