There is probably a delay timer or other circuit in the control board that prevents the running. Whatever the cause, I would install a return duct thermostat that would sense an upper limit of air coming to that return duct, perhaps 72F, to disconnect the 1st-stage heat compressor relay at the outside unit when the stove is on. That way, operation would be automatic changeover from heat pump to wood. If the fire died down, then the compressor would take over again. The duct thermostat would require a bypass switch to enable the coompressor for summer operation.