In a microwave-safe bowl, melt 20-oz. candy coating; stir until smooth. Stir in corn syrup just until blended. Spread onto a sheet of waxed paper to 3/8-in. thickness (about a 16-in. x 8-in. rectangle). Let stand, uncovered, at room temperature for 2 hours or until dry to the touch. Wrap tightly with plastic wrap; let stand overnight. Use immediately or store for up to 2 weeks.
Melt 10-oz. candy coating; stir until smooth. Completely coat pretzel sticks; place on a wire rack. Chill for 10 minutes. Set remaining melted coating aside.
Be certain plastic cover is clean and dry. Place two dampened paper towels in the bottom of a 1-1/2-qt. bowl. Position cover on the towels (to hold it in place). Place ends of the candy-coated pretzels around outer edge of cover, resting the other ends against the side of the bowl to form the supports for basket sides.
Spoon some of the reserved candy coating into plastic cover until it is 1/8 in. from the top and surrounds all of the pretzels. Chill until firm, about 30 minutes. Remove from the bowl and discard paper towels. Carefully loosen edges of plastic cover and remove. Set base on waxed paper.
Knead a 1-in. ball of chocolate clay until pliable but not sticky. Roll into a 1/4-in. rope. Beginning on the inside of a pretzel, loosely weave rope around pretzels. Repeat, adding the next rope by overlapping slightly and pressing ends together. (Always end one rope and begin the next on the inside of a pretzel.) Continue to weave between pretzels until the top of the pretzels is reached, ending the last rope on the inside of a pretzel.
Make three ropes about 20 in. long; braid and set aside. Remelt reserved coating; place a drop on the top of each pretzel. Lay braided ropes on top, blending the ends to create a finished edge. If pretzels break, "reglue" with melted coating.
For basket handle, make one rope about 15 in. long. Push headband into rope to within 1 in. of each end; mold rope around headband to cover. Insert uncovered ends of headband into top braid of basket. Decorate with ribbon if desired.