If the chances of killing an avatar stay low then it should be ok. If lower ranks have 1 attempts per full Chancellor term and higher ranks 2 then this should eliminate these "just come back and see you've had 10 assassination attempts on you" moments. Unsuccessful attempts should affect characters also (perhaps they can not be moved 1-2 turns because character is trying to find other assassins who could want to kill him).
This is just a suggestion but perhaps instead of one huuuge family tree we could have only one small with Basileus and his family and the second one with Heirs family. It took a looong time to put together that FT that you can see in the Library at the moment(there is no in-game button that could do it like that unfortunately)!
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