Egg Hunt

a cryptic puzzle by Emily Cox and Henry Rathvon

Solution
Solvers are invited on an egg hunt, to be conducted within the boundaries of this puzzle's diagram. The unclued Across entry in the middle of the diagram tells how many eggs are hidden. Clue answers include six proper nouns; 19 Across is a variant spelling. Diagram entries include five proper nouns: 28 Across is a variant spelling.

Across

  • 1.
    Shot thirdly, firstly, fourthly, and lastly (3)
  • 5.
    Hoax involving middle of World Series (6)
  • 10.
    Gold crown with a wreath initially cropped (7)
  • 11.
    Note incomplete remedy, and come back (5)
  • 12.
    Name of a woman, say, in South America (6)
  • 13.
    Metal I turned into iron is limited (6)
  • 14.
    Public transportation adopts railroad stickers (5)
  • 16.
    Stoneworkers more recently collecting Social Security? Quite the opposite (7)
  • 18.
    Lawful walk? (5)
  • 19.
    Males notice female in an orgy (5)
  • 20.
    Road circling eastern spring (6)
  • 25.
    Philosophers with timeless platforms (5)
  • 27.
    Take a piece away from part of lunar module (5)
  • 28.
    Study Paradise Unbegun (3)
  • 30.
    Book in green is seen in translation (7)
  • 33.
    Burns novel finally found in piles (6)
  • 34.
    Circus performer holding elephant's tail in palm (5)
  • 35.
    The Mark of Zorro, in general, has oomph (4)
  • 36.
    Shuts up some swans (4)
  • 37.
    Designed the last covert action (7)
  • 38.
    Sally canceling all checks from organizations (7)
  • 39.
    Growth in both ends of city street (4)

Down

  • 1.
    Cross questions from assignments (5)
  • 2.
    Missing a home-run king? That's bad (8)
  • 3.
    Shakespearean woman's anger exploded (5)
  • 4.
    Low spot containing uranium and deuterium is thought worthwhile (6)
  • 5.
    Singer's face, blackened, was outstanding (7)
  • 6.
    Gun lacking central part causes stir (4)
  • 7.
    Freezing (1 Celsius) in Gulf (5)
  • 8.
    Party snacks in jar overturned (4)
  • 9.
    Heard implement for chefs is better (7)
  • 15.
    August is dry, and half of June (6)
  • 17.
    Small bug raised bites (5)
  • 21.
    Related versions of five songs about New Testament (8)
  • 22.
    A certain King's shot? (3)
  • 23.
    Courts harboring the Spanish peoples of Europe (5)
  • 24.
    Disgustingly, wine gets left in the Big Apple (7)
  • 26.
    Box with American in Rocky scene (6)
  • 27.
    Abstract nude with red below (5)
  • 29.
    Largest estate houses some noble Italians (5)
  • 31.
    Sense the sound of a breeze over tree's top (5)
  • 32.
    Make out in mind-reading club? (4)