Food processing apparatuses and associated methods are disclosed herein. In one embodiment, a fish processing apparatus (10) includes two sets of shim magazines (20a, 20b) on the opposite sides of mold(s) for making food products. Food shuttles (114) alternate in transporting food shims from their corresponding shim magazines (20a, 20b) to a position under the mold(s). An actuator (30) presses the mold(s) against the food shim to form food products. The force of the mold(s) can be controlled to improve separation of the food products from the food shim. Formed food products fall on a conveyor (112), which transports them away from the apparatus (10) for further processing.