At least 24 hours before making the ice cream, place bowl of ice cream maker in freezer.
Hull and quarter 6 ounces (about 1 cup) strawberries; slice quarters crosswise into very thin pieces. In a mixing bowl, combine strawberries with ½ cup sugar and alcohol, and let stand in refrigerator for at least 2 hours and up to 2 days.
Hull remaining strawberries and purée at high speed in a blender until very smooth, about 30 seconds. Strain through a fine mesh strainer to filter out all seeds and fibers, then measure and reserve 1 ½ cups purée. Extra purée, if there is any, can be put to another use.
In a clean mixing bowl, whisk together 1 ½ cups strawberry purée with half and half, corn syrup, and remaining ¾ cup sugar until fully combined. Add salt to taste, and, if mixture is too sweet, a few drops of lemon juice.
Chill in freezer or ice bath until base is very cold, at least 45°F, then churn in ice cream maker according to manufacturer's instructions. In the last few minutes of churning, retrieve strawberry pieces from the refrigerator, strain off syrup, and add pieces to the churn. Transfer ice cream to airtight container and chill in freezer for at least 4 hours before serving. Yield: 1 quart.