Chill a rocks glass for service. Combine the sugar water, rye, and Peychaud’s in a mixing glass with ice. Stir (or stab) five or six times, being careful not to over-chill or over-dilute the drink. Dump the ice from the chilling service glass. Add 2 or 3 drops of Herbsaint and swirl to coat. Discard extra. Strain the rye mixture into the service glass and coat the rim with lemon oil. Extrude more lemon oil into the drink. Discard peel and serve.