Cut cheeks (peel, pith, small bit of fruit) off the four sides of an orange - bonus if it's a Valencia or Seville. Add ingredients to glass, drop in four orange cheeks, add ice and shake (to integrate the orgeat). Double strain into a coupe, and garnish with a thin orange slice.
I'm hoping that this builds a nutty-citrus accord that fights the buttery-oily arrack. Manzanilla sherry is like a super-fino, and hopefully the detailed instructions get enough orange into the drink without having to add orange juice.