[spaghetti]

bottarga tastes delicious: it's the name of fish eggs (tuna or golden mullet) used as a pasta dressing. An even more challenging taste is lattume: the sperm of the male tuna, very good on spaghetti (oops, did I really say that?!)
I'm not a sicilian, and I just had one sperfishing holiday on that Island, but it was in the south east. Don' know about the strait of Messina, but I think there's a heavy boat/ship traffic since the straight is narrow. Eolie will be quieter, as june is not yet full season for tourism.
In june you're likely to meet AJ's (our Aj's weigh up to 50 kilograms)and for sure the sicilians have a great tradition in spearfishing and freediving, so I bet that with an expert local boatman/buddy you will be satisfied with the experience.