Line an 8-by-4-by-3-inch loaf pan with plastic wrap, leaving enough overhang in each direction to completely cover the top. Measure out 2/3 cup of the strawberry preserves. Set both aside.
Beat the cream cheese in the bowl of a stand mixer fitted with the paddle attachment on high until fluffy, about 4 minutes, stopping to scrape down the sides of the bowl as needed. Add the sour cream and lemon zest and beat until combined, about 30 seconds more. Transfer to a large mixing bowl.
Swap the paddle for the whisk and whip 1/2 cup of the cream along with the powdered sugar on medium-high until stiff peaks form, about 3 minutes. Fold into the cream cheese mixture and transfer to a zip-top bag.
Cover the bottom of the prepared loaf pan with a layer of graham crackers. Snip the corner of the zip-top bag and pipe in approximately 1/4 to 1/2 cup of the whipped cream mixture and smooth with a spoon or spatula. (It's totally fine to eyeball this; just know you'll end up with 6 cream layers.) Top with about 3 tablespoons of preserves (again, it's fine to eyeball), followed by 1/2 teaspoon of pepper and another layer of whipped cream.
Continue layering—crackers, whipped cream, preserves, pepper, whipped cream, crackers—until you have 4 layers of graham crackers (see Cook's Notes). Fold the excess plastic wrap over the cake and refrigerate 8 hours and up to 24.
When ready to serve, whip the remaining 1 cup cream in the bowl of a stand mixer on medium-high until stiff peaks have almost formed. Drop the mixer to low and work in the remaining 1/3 cup strawberry preserves and 1 teaspoon black pepper. Boost the speed back to medium-high until stiff peaks form.
Pull back the plastic wrap and invert the cake onto a serving dish. Remove the plastic wrap completely and frost with the strawberry whipped cream. Slice and serve immediately.
What's most important is that the crackers always sit between cream layers, never jam. The fat in the cream keeps the crackers from becoming too soggy