It doesn't seem like a bad idea to me, only that it would take a long time I think.
Something different:
I 've been thinking of the idea of letting bad teams survive in the cup a little longer. Though I think this is just an idea for the future and I don't know what to do with the time yet 'cause it's too short. Maybe it would be easier to start having a cup over 2 seasons since there will eventually get more managers.
My idea: to start the cup with groups of 8 teams randomly chosen which only play once against each other. 2 go over to the next round. Then you can go to instant elimination, but in this way even bad teams get a chance of meeting a big team which brings some money in, and they get to play 7 matches.
This off course needs a lot more time than the one season cup played now so this suggestion might be useless.
Also it could give problems with the maths, because I believe Soccerproject is now build so that every team gets to participate to the Cup. So I don't know, but it's just the idea of a group I like.