I'm no expert here but reading your post had look at the files to find the mechanism beyond the election of the pope. I haven't it so far but I found this line in the descr_sm_factions.txt:

has_family_tree no

I wonder if it can be of use somehow

Only two factions have no on this line, Papal States and Slaves. Did anyone do tests with this option? if yes, what possibilities are there ?

Also, what about the capability of the Pope to promote Priests to Cardinals?