Combine water, almonds, sugar, rice, vanilla, cinnamon, and salt in bowl. Cover and let sit at room temperature for at least 12 hours or up to 24 hours.

Set fine-mesh strainer over 8-cup liquid measuring cup and line with triple layer of cheesecloth that overhangs edges. Process almond mixture in blender until smooth, 30 to 60 seconds, scraping down sides of blender jar as needed.

Transfer mixture to prepared strainer and let drain until liquid no longer runs freely, about 5 minutes. Pull edges of cheesecloth together to form pouch, then firmly squeeze pouch to extract as much liquid from pulp as possible; discard pulp. You should have 2 cups liquid. Stir in rum and cream, cover, and refrigerate until completely chilled, at least 1 hour or up to 2 days. Stir to recombine, then pour into chilled collins glasses filled with ice. Garnish with lime slices and cinnamon and serve.