This demand isn't local, and that changes everything. Someone shipping bottles isn't competing with the shop down the road but with other producers, so variety, harvest and explanation count for far more than any mention of a town.
The new harvest is a seasonal peak in its own right. People search for fresh oil from November onwards, and publishing that page in January means missing the part of the year when most of the buying happens.
Use beats description. "Best olive oil for cooking", "olive oil gift set", "olive oil in a tin": those are the searches that actually end in a purchase, and they're absent from almost every producer's website.
Certification is worth a page where it exists. A protected designation is typed out in full by people who already know what they want, and explaining what the rules require persuades more than a paragraph about the family.