I find that garlic, left whole and kept out of the refrigerator, keeps for months. I keep mine in a cookie tin once it is dry. Mince it when you need it, and use the freshly minced garlic in the same way you're using the dry. Don't try to dry minced garlic yourself. There's no benefit for you, and plenty of risk.
Instructions for oil-preserved garlic go on and on about botulism, which can be in anything that had ground contact, and which we cannot detect by smell or sight, unlike mould or other forms of spoiling. Risking that just so you can do all the mincing at once instead of as you need the garlic does not seem like a good idea.