Jared Hirsch of Sidebar and Nickel Dime Syrups shared his recipe for lime cordial that requires no zesting of limes. 

Lime Cordial
From Jared Hirsch of Sidebar

• 4 cups lime juice (reserve lime shells)
• 3 cups cane sugar
• 4oz vodka

Using a cleaned jar saved from our olives, we pour the ingredients over the juiced lime shells (unpeeled) and refrigerate for 2 days before straining out the liquid, re-juicing the limes to extract as much cordial as possible. 

I've tried both just lime peels and whole spent limes and found very little difference, preferring the unpeeled limes the best, which conveniently is less work.

Recipes that Use Lime Cordial Beyond the Gimlet
From Jared Hirsch of Sidebar

Foolish Whispers
1oz Jamaican pot still rum (Doctor Bird preferred)
1oz Spanish light rum (Flor de Caña 4yr preferred)
.5oz Aperol
1oz lime cordial
Shaken over ice, served up, garnished with a grapefruit twist

Mezcal Gimlet
2oz Mezcal Espadin
1.5oz lime cordial
Shaken over ice, served up, garnished with a lime twist

Perennial Underdog
1oz Jamaican pot still rum (Doctor Bord Preferred)
1oz Bajan dark rum (Mt. Gay Black Barrel preferred
1.5oz lime cordial
Shaken over ice, served up, garnished with a lime wheel

Run, Run, Run, Jump
2oz Bajan dark rum (Mt. Gay Black Barrel preferred
1.5oz lime cordial
1oz Darjeeling tea (1 Tbsp tea, 1 Cup boiling water, steeped 5 min)
Shaken over ice, served tall over crushed ice with a straw, and garnished with a mint sprig.