Adjust oven rack to lower-middle position and heat oven to 325 degrees. Spray bottom and sides of 9-inch springform pan evenly with nonstick cooking spray. Pulse crackers, sugar, and spices in food processor until evenly and finely ground, about fifteen 2-second pulses. Transfer crumbs to medium bowl, drizzle melted butter over, and mix with rubber spatula until evenly moistened. Turn crumbs into prepared springform pan and, using hand, spread crumbs into even layer. Using flat-bottomed ramekin or drinking glass, press crumbs evenly into pan bottom, then use a soup spoon to press and smooth crumbs into edges of pan. Bake until fragrant and browned about the edges, about 15 minutes. Cool on wire rack while making filling.

Bring about 4 quarts water to simmer in stockpot. Whisk sugar, spices, and salt in small bowl; set aside. To dry sweet potato, line baking sheet with triple layer of paper towels. Spread sweet potato on paper towels in roughly even layer. Cover sweet potato with second triple layer of paper towels and press firmly until paper towels are saturated. Peel back top layer of towels and discard. Grasp bottom towels and fold sweet potato in half; peel back towels. Repeat and flip sweet potato onto baking sheet; discard towel.

In standing mixer fitted with flat beater, beat cream cheese at medium speed to break up and soften slightly, about 1 minute. Scrape beater and bottom and sides of bowl well with rubber spatula. Add about one third of sugar mixture and beat at medium-low speed until combined, about 1 minute; scrape bowl and add remaining sugar in two additions, scraping bowl after each addition. Add sweet potato, vanilla, and lemon juice and beat at medium speed until combined, about 45 seconds; scrape bowl. Add 3 eggs and beat at medium-low until incorporated, about 1 minute; scrape bowl. Add remaining 2 eggs and beat at medium-low until incorporated, about 45 seconds; scrape bowl. Add heavy cream and beat at low speed until combined, about 45 seconds. Using rubber spatula, scrape bottom and sides of bowl and give final stir by hand.

Set springform pan with cooled crust on 18-inch-square doubled layer heavy-duty foil and wrap bottom and sides with foil; set wrapped springform pan in roasting pan. Pour filling into springform pan and smooth surface; set roasting pan in oven and pour enough boiling water to come about halfway up side of springform pan. Bake until center of cake is slightly wobbly when pan is shaken, and center of cake registers 145 to 150 degrees on instant-read thermometer, about 1 ½ hours. Set roasting pan on wire rack and use paring knife to loosen cake from sides of pan. Cool until water is just warm, about 45 minutes. Remove springform pan from water bath, discard foil, and set on wire rack; continue to cool until barely warm, about 3 hours. Wrap with plastic wrap and refrigerate until chilled, at least 4 hours or up to 3 days.