I may have sounded overly negative in my first detailed post. I was trying to highlight issues another storyguide should think of before running the tourney.
But globally, my players enjoyed the concept and the challenges. It was mostly I, as storyguide, that was somewhat unsatisfied with the hesitations and difficult adjudications that I had to do. Contrary to Leonis, I believe that a little more "playtesting" might have urged a few clarifications to be included in the rules.
If people really want to simplify the tourney to a maximum, I think it shouldn't require a system: just rank all teams according to roughly perceived overall competence or covenant might, adding a few surprises that would show the random element or specific secret needs for your saga stories.
I could have done that, but I was curious to see where the whole system would lead me. I actually started with a spreadsheet with all teams cross-referenced with all competitions, I gave each of them marks from A to F on each event depending on how good they should be, then I ranked all A's if any, then all B's if any... etc. for each event. I figured out points and number of magi per team, then I added everything to get their final global rank. Then of course I made a nice catalogue of tropaea to choose from, region/amount/type of vis + books + items, striking out those chosen by NPCs in between the PC's choices.
I know, I should have spent those several hours on more sensible activities 
As I said, we had fun in the end.