Put green meringue in a piping bag fitted with a ⅜" star tip. Start with a 1 ½"-wide star, then pipe two more stars on top of the first, each ½" smaller than the last, to form a three-tiered Christmas tree. Repeat steps to make additional trees.
Put plain meringue in a piping bag fitted with a ⅜" round tip. Pipe several 1 ½"-wide mounds and ½" x 1 ½" sticks to form mushroom caps and stems. Once the meringue pieces have baked and cooled, fit stems into bottoms of caps.
Place hot cake on a large kitchen towel dusted with confectioners' sugar; dust cake with more sugar. Starting with one narrow end, roll cake and towel together into a tight cylinder; let cool completely. Gently unroll cake.
Brush rum syrup evenly over the cake with a pastry brush. Using an offset spatula, spread buttercream evenly over the cake, leaving a 1" border along the top edge so that the roll will close neatly and the buttercream will remain inside.
Starting with the edge nearest you, roll the cake, taking care not to apply too much pressure, so the buttercream stays inside the roll. Transfer the cake roll to a serving platter, seam side down, and chill to set.
Using a serrated knife, cut 3" off one end of cake at a 30° angle. Trim other end of cake to make it flat. Remove angled end and spread its flat side with buttercream—this will help it stick to the top of the cake.