Place 8½ by 4½-inch loaf pan in freezer.

Combine peaches, ½ cup sugar, ½ teaspoon lemon juice, and salt in bowl; let sit until about ½ cup liquid accumulates in bowl and peaches soften slightly, 1 to 1½ hours.

Drain peaches in fine-mesh strainer set over second bowl. Reserve ½ cup liquid; discard remaining liquid.

Process drained peaches in blender until smooth, about 1 minute.

Transfer ½ cup peach puree to small saucepan; reserve remaining puree.

Add ½ cup sugar and remaining 2 tablespoons lemon juice to saucepan and bring mixture to boil over medium heat.

Cook, stirring and scraping bottom of saucepan constantly with rubber spatula, until mixture turns deep orange color, becomes translucent, and registers 218 to 220 degrees, 6 to 8 minutes.

Transfer cooked peach mixture to bowl; let cool slightly, cover, and refrigerate until needed.

Bring reserved drained peach liquid to simmer in now-empty saucepan over medium heat and cook, stirring often, until liquid is thick and syrupy and registers 218 to 220 degrees, 6 to 8 minutes.

Transfer syrup to large bowl.

Add half-and-half, sour cream, corn syrup, vodka, remaining ⅔ cup sugar, and remaining reserved uncooked peach puree and whisk until smooth, about 30 seconds.

Cover and refrigerate ice cream base until temperature registers 40 degrees, about 4 hours.

Transfer ice cream base to ice cream maker and churn until mixture resembles thick soft-serve ice cream, 25 to 30 minutes.

Spread one-third of ice cream in even layer in prepared loaf pan.

Drizzle one-third of reserved cooked peach mixture evenly over ice cream.

Repeat 2 more times with remaining ice cream and peach mixture.

Drag skewer through ice cream (in rough zigzag and circular patterns all the way to bottom of pan) to create swirls.

Freeze ice cream until firm, at least 2 hours.

Serve.