In a nine person race, fair means that a constituency which is composed of only a little more than 1/9th the voting population has a 'fair' chance of getting one seat. By dividing the election into a 5 person race and a 4 person race, the constituency has to be composed of at little more than 1/5 or 1/4 the voting population. Dividing the race into three would make matters worse.
You are always going to have continuity. What is the chance that everyone will be voted out? And if they are, maybe that is also a good thing? Continuity is something that can be decided by a vote, it doesn't have to be enforced by process.
Again, my points are not that we should go with the 'most provably fair' system possible. But the two details I have pointed out are provably unfair to minority voices. Note that one, that is 1/9, vote of 'no' on any TIP, forces 2/3 voting. That means the intent it to support minority voices down to this level, and the two voting issues I am pointing out work against that intent.