Make filling: In a large bowl, combine strawberries, 2 tbsp. sugar, the zest, and juice. Let sit 10 minutes.
In a medium bowl, whisk cream with remaining 4 tbsp. sugar until it holds a stiff peak.
Assemble cake: Using a serrated knife, slice both cake layers in half horizontally. Set rounded tops aside to use as middle layers. Dollop 1 tbsp. whipped cream onto the center of a cake stand (to hold cake in place). Place 1 of remaining layers on stand, cut side up. Spread with about 3 tbsp. jam. Sprinkle with about one-quarter of the sweetened strawberries, along with some juice. Then dollop one-quarter of the cream over strawberries. Repeat with second and third cake layers, using the reserved rounded tops.
Place the remaining layer on the top of the cake, cut side down. Mound the remaining whipped cream in the center and spread to about 1 in. from the edge, then sprinkle with remaining strawberries.