You got it....all correct ! The difference between hard and soft mode is how it was selected. Its described as soft if the EEC automatically reverted to alternate with no pilot input. Its hard if the pilot selected the alternate mode manually. In soft at a fixed thrust lever position thrust does not change. In hard at a fixed thrust lever position thrust may change to set commanded N1 when the alternate button is pressed. Hence move the lever back first to prevent possible overboost.