I couldn't stand leaving this savegame like this, so I just restarted as Venice. A quick look at the tech screen showed that I started halfway to Trade Practices III, so no tradezone penalty this time. I guess the Old Gods DLC broke my save (retarded).
Anyway...
I started with finding suitable breeding stock for the male Contarini's. All of them, because with seniority succession that's highly relevant. I got myself a strong (+3 to every stat) spymaster wife, and the most prominent rival family head is already disposed of.
My breeding programme pays off soon:
This isn't relevant for now under seniority succession, but at least it's a promising start. My goal for now is to get a family trade zone in the whole Adriatic. I'll need to find a way to steal some opposing family holdings to make that work.