The whole piyut is composed of pesukim and allegories, which are artistically formatted in an alphabetical order. However, the פסוק of שמחים fits with the style of the song there, and ש is replaceable with a ס - they are interchangeable
It's a good question and actually has an interesting answer.
The reason why this particular detail is important and can't be changed is because it relates to two of the fundamental Principles of Jewish faith, the coming of Moshiach and the resurrection of the dead.
From the 10th to the 22nd lines are all describing and/or relating to what is mentioned in ...
According to the rabbis and the Rav that I learned from, one cannot simply declare a seudat mitzvah by including praises of HaShem. We praise HaShem anyways when we bentsch. Even Rosh Chodesh meals are not considered seudat mitzvot according to my Rav.