Possibly the difference has to do with the structure of the piyutim in each case.
The halachah is that you're allowed to add any kind of requests, even private ones, in the middle berachos of Shemoneh Esrei (Shulchan Aruch, Orach Chaim 119:1), and you can add public ones even in the first and last ones (ibid. 112:1). In either case, though, the addition has to be thematically related to the berachah.
Arguably, then, the relatively short paragraphs inserted into the berachos, in the instances mentioned in the question, are closely related enough to their parent berachos to not need any kind of special "request for permission" (which is basically what Misod is). In fact, I have a volume of ancient piyutim (found in the Cairo genizah) for individual Shabbasos throughout the year (מחזורי שבעתות לסדרים ולפרשות, ed. Shulamit Elitzur), from which it seems that there were times and places where they used these as replacements for the original bodies of the berachos (i.e., the chazzan would begin his repetition of Shemoneh Esrei by saying a four- or five-line piyut and then continue בא"י מגן אברהם, etc.) - so that there is precedent for considering these to be basically alternate versions of the berachos rather than interpolations.
Whereas when there are longer piyutim, even though the ones inserted in the berachos do (usually) end with a phrase containing the main theme of the berachah, it may be much harder to justify them on that basis.