Reading through the timeline, it appears that the 6th Emperor (seen in Panzer Dragoon Zwei) was the brother of the 3rd Emperor. When the 3rd Emperor died, the era of the 4th Emperor was weaker and he died a year later from an illness. The 5th Emperor then ascended the throne, but died within the year via an accident with an Ancient engine.
Assuming that the 4th and 5th Emperors were son and grandson of the 3rd Emperor (or perhaps both sons of the 3rd Emperor), it seems suspicious that both would die so quickly after the 3rd Emperor’s death. Although I have no evidence, I suspect their deaths might have been an inside job. The 6th Emperor could have poisoned the 4th Emperor and arranged for the 5th Emperor to have an “accident” in order to gain the power of the throne for himself. If so, he could be considered a much more ruthless emperor than I originally thought, not just invading Meccania, but offing his rivals as well. By contrast, the 7th Emperor didn’t need to be quite as ruthless since the rival nations appeared to have all been conquered by the time he ascended the throne.