Preheat oven to 375°.
Pierce 10 holes on one side of the bottom of a 13 x 9-inch disposable aluminum foil pan. Place holes over element on cooktop; place wood chips over holes inside pan. Heat element under holes to medium-high; let burn 1 minute or until chips begin to smoke. Arrange cherries on opposite end of pan. Cover pan with foil. Reduce heat to low; smoke cherries 5 minutes. Remove from heat; uncover.
Combine almond paste and 1 tablespoon sugar; beat with a mixer at medium speed until mixture resembles damp sand. Add cream cheese, vanilla, and salt; beat until combined.
Place 1 phyllo sheet on a work surface (cover remaining dough to keep from drying); lightly brush with butter. Sprinkle with 1/2 teaspoon sugar. Repeat layers with remaining phyllo, butter (save a little butter for the outsides), and sugar. Cut 12 (3 1/2 x 3-inch) rectangles through phyllo layers using a pizza cutter or sharp knife. Place 1 teaspoon almond mixture in the center of each phyllo stack; press 1 cherry, stem up, into almond mixture. Gather corners of phyllo, and press around stem to seal, forming a pouch. Gently brush pouch with remaining butter. Place pouches on a baking sheet lined with parchment paper. Bake at 375° for 13 minutes or until crisp. Cool on pan on a wire rack.