The Idea in Brief
The following explanation provides one tentative view based on Jewish oral tradition. That is, the Babylonian Talmud provides one possible explanation as to why there are two paragogic nuns in this verse.
Discussion
First, the editors of the Masoretic Text finalized their written work during the Ninth and Tenth Centuries of the current era. Their legacy is not only the documentation of the system of accents and cantillation, but their thorough indexing of the Biblical texts as well, which we term the Massorah. Gérard Weil (2001), who translated the Massorah at the request of the editors of the Biblia Stuttgartensia Hebraica, had written the following regarding the Masoretes and their legacy -
La Massorah est le fruit le plus concret en matière d’étude du texte biblique qui a été produit par les nombreuses générations de maîtres et d’exégètes que la Synagogue a connus. Plus de dix siècles de recherches fidèles ont déposé dans les marges des manuscrits et entre les colonnes des livres, comme au fond des mers les sédiments marins, les couches successives des connaissances acquises dans les écoles de la Bible. Un nombre incommensurable d’heures d’étude de jour et, combien plus encore, de veilles de nuit ont été consacrées à la conservation, à l’authentication et à la transmission, si ce n’est à la connaissance du Texte.
[In the study of the Biblical text, the Massorah is the most significant outcome to have emerged from several generations of teachers and scholars ever known by the Synogogue. More than ten centuries of faithful research are deposited in the margins of the manuscripts and between the columns of the books like the sediment on the sea floor, successive layers of knowledge acquired in the schools of the Bible. An immeasurable number of hours of study by day and, how much more, vigils by night were devoted to the preservation, authentication and transmission, if not to the knowledge of text.]
Weil acknowledged that the Masoretes approached the Biblical Texts through the lens of Jewish tradition. They lived and worked at the time when the Jewish Talmud was already in its final stages of completion. One contemporary of the Masoretes was Rabbi Shlomo Yitzchaki ("Rashi"), who lived in France, and whose legacy and commentary form part of the Jewish Talmud as known today. Thus the oral tradition of the Talmud provided the foundation of the Masoretes as they approached the Biblical Texts. Kelly et al. (1998) note the following.

In summary, the Masoretes operated in the "milieu" of the legacy of Jewish tradition, which was codified in the Talmud.
The Talmud
The Babylonian Talmud relates the following regarding the interpretation of the verse at hand. This following citation comes from Folio 55B of b. Sabbat 5:4, XII:15-16 as translated by Neusner (2011).

The Talmudic rabbis understood the literal sense of the Hebrew Texts (proto-Masoretic) to refer to the third person masculine plural of the verbs "to do" and "to lay" (which both carry the paragogic nun in this verse). The references to 1 Sam 2:24 and 1 Sam 2:12 in the dialog is additional proof that the Talmudic rabbis understood the literal sense of the Hebrew Texts in context as referring to the third person masculine plural--that is, the two sons of Eli: Phineas and Hophni.
However, these rabbis seem to be drawing from proto-Masoretic texts relating to the same source material used for translating the LXX. That is, the subject of the last clause of 1 Sam 2:24 is not third person plural, but third person singular in the LXX. In other words, the rabbis speaking in Para F and Para G (above) are alluding to someone in the singular (Hophni) not serving God, and not plural (Hophni and Phineas). Tan and deSilva (2009) relate why -
The Hebrew reads "the people of the LORD spreading" as the object of "hearing," instead of the result clause in the LXX of "so that the people do not serve God." The difference comes from reading a daleth in a participial form of עבד ("to serve") rather than a resh in participial form of עבר ("to cause to transmit" in this case).
As already noted earlier, written punctuation did not appear in the Hebrew Scriptures until the Masoretic Period.
While modern readers of English translations of the LXX would understand "people" in the context of this verse in an aggregate sense -- such as the people of Israel in general -- the Talmudic rabbis used this ambiguity to advance their nuanced interpretation. That is, Hophni was the philanderer who was taking advantage of the female attendants of the Tabernacle, whereas Phineas, his brother, by not intervening, had provided tacit consent to his wrongdoing. Thus Samuel, who authored the book bearing his name (please see Babylonian Talmud Folio 14B and Folio 15A of b. Baba Batra 1:XI-XV), had included them both culpable in the literal sense of the text (as the Talmudic rabbis as noted had correctly observed). The paragogic nun, therefore, provides the reader the necessary indicator that the verbs carry nuanced meaning, for which the reader today must turn to the Talmud for the Jewish oral tradition behind this verse.
Conclusion
The hypothesis described in this posting is one tentative approach for understanding why two paragogic nuns appear in the verse at hand. In this verse, the paragogic nuns provide the necessary but nuanced grammatical appendage that signals to the reader that there is extrabiblical (oral proto-Masoretic tradition) bearing on the verse and its interpretation. Thus the appearance of the paragogic nun may be related to more than just the semantic and grammatical structure of the verse and its words (in cases where the nun complements and closes the vowel stress when preceding an aspirant consonant, and so forth).
In summary, this hypothesis provides one tentative view based on Jewish oral tradition. Further study will have to occur (such as unpacking the textual and manuscript variants for this verse as noted in the critical apparatus of the Biblia Stuttgartensia Hebraica).
References:
Kelley, P. H., Mynatt, D. S., & Crawford, T. G. (1998). The Masorah of Biblia Hebraica Stuttgartensia: Introduction and Annotated Glossary. Grand Rapids, MI: William B. Eerdmans Publishing Company, 14.
Neusner, Jacob (2011). The Babylonian Talmud: A Translation and Commentary. Peabody, MA: Hendrickson Publishers.
Tan, R., & deSilva, D. A., Logos Bible Software. (2009). The Lexham Greek-English Interlinear Septuagint. Logos Bible Software.
Weil, Gerard E. (2001). Massorah Gedolah: Manuscrit B. 19a de Léningrad. Rome: Pontificium Institutum Biblicum, XIII.