Alcohol has a much lower freezing point and will never freeze properly in a standard freezer. Therefore, you can only add a little Rum. Alternatively, you can try adding more Rum and making a Granita instead, where you pour out your mix into shallow trays and then scrape them with a fork, freeze again and then scrape again into small cups when ready. However, you still won’t be able to freeze the exact recipe of a Daiquiri as there will still be too much rum.