One possible issue to resolve the 'need to remove bad emperor without coup/civil war' could be the concept of retirement. In my original draft Andreas Niketas lived into his 90s, but in his mid 70s retired. He retained all the ceremonial trappings of being an Emperor but his heir had all the power. If something like that became a tradition, perhaps bad emperors could be retired on grounds of incompetence rather than the original factor of age. The concept of co-emperorship is perfect for this. Obviously one issue with this is that it requires a heir to fill the slot of the retiree.
Well, if an heir does not exist, the Senate (or the people itself) can elect a leader from a different family.
for example, the last Angelos Emperor is forced to retire due to extreme disgusting incompetence, and the People elect the Komnenos Emperor back into power.
you will, of course, allow females to become leaders on occasion? i would love to have a Roman equivalent of Elizabeth II. but more powerful. and long reigning.