I found another helpful bit from La Bible D’Alexandrie: Les Douze Prophètes this afternoon. Here, they connect the ship’s cargo hold into which Jonah went down to sleep in 1:5 with the belly of Hades in 2:3. Though there is a conceptual link within the MT, that link is made more explicit by the LXX translator with the translation of בתן with κοιλία. On page 147, the commentators write:

~ “fut dans le ventre”: le mot koilia, “ventre”, repris en 2, 2 et 2, 3 rappelle koilē, “cale” de 1, 5, suggérant une assimilation  propre au grec entre le ventre du navire, le ventre du monstre marin et le ventre de l’Hadès. Le TM a deux mots différents pour désigner l’ “intérieur”, mē’īm, du poisson (2, 1; 2, 2) et les “entrailles”, beten, de l’Hadès (2, 3).

~ “was in the belly”: the word koilia, “belly,” taken in 2:2 and 2:3, recalls koilē, “hold” of 1:5, suggesting an assimilation unique to the Greek between the belly of the ship, the belly of the sea-monster, and the belly of Hades. The MT with two different words for the designation of the “inside,” mē‘īm, of the fish (2:1, 2) and the “entrails,” beten, of Hades (2:3).

By establishing the connection between Hades and the ship’s cargo hold, the translator strengthens the author’s depiction of Jonah’s descent away from God. This descent, at each stage, is depicted as a descent into death. Jonah go down into Joppa, finds a ship and goes down/embarks, goes down into the ship’s hold, goes down into a deep sleep, is cast overboard and goes down into the depths of the sea where he claims that he is in the belly of Hades.