System and method for producing fluids from a hydrocarbon reservoir where an injector well segment and parallel underlying producer well segment are both completed with slotted liners. The injector and producer segments are logically partitioned into corresponding sections to define a plurality of injector-producer section pairs. Injection tubing strings supply stimulating fluid (e.g., saturated steam) to associated sections of the injector segment for injection into the hydrocarbon reservoir. Surface-located control devices control the pressure of the stimulating fluid flowing through the respective injection tubing strings. Production tubing strings (with the aid of artificial lift) carry fluids produced from associated sections of the producer segment. A plurality of controllers is provided for the injector-producer section pairs to control at least one process variable (e.g., interwell subcool temperature) associated with respective injector-producer section pairs over time by adjusting control variables that dictate operation of the control devices for the injection tubing strings.