The meaning of malkut is very important as it means that where it appears in the OT and in particular its use in Daniel can alter the interpretation and history of that book, Daniel. You apparently fail to recognize that this Aramaic word means more than 'reign' and is a descriptor of that reign. Tradition by as shown by the commentaries, biblical and Josephus all place Jehoiakim's third year not at the beginning as the apostates claim but in fact at the end which led to the death of Jehoiakim replaced by Jehoiachin and the first siege of Jerusalem with the first deportattion of Jewry to Babylon.
You keep trying to assert that malkut carries more meaning than 'duration', but it makes absolutely no difference to your argument. Jehoiakim's malkut still started at the same point regardless of what meaning you are assigning to it (since it doesn't mean 'paying tribute to some other guy'), and there is nothing in Daniel to suggest that he was malkutting in some other sense further down the track.
So it seems that your entire argument relies completely on Jewish 'traditions of men'.
Josephus makes no actual reference to say that this third year was actually Jehoiakim's third-last.