I think I learned something cool. Pilgrimage distance (and the number of events you get) is associated with where you put your leader and not where your capital is. Typically I've been frustrated playing as Byzantium because I usually just get 1 event before I arrive in Jerusalem, the farthest pilgrimage site as Orthodox. But then I had the idea to have my emperor lead an army in Spain before I selected the Go on Pilgrimage decision. Then I got 5 decisions! Wow! I think I'm going to do a pilgrimage from Iceland next. 
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