Instead of adding the Conference League, I suggest a slightly different format for the Champions League: every club has its associated ELO rating only influenced by official games, as in clubelo.com (works similar to chess ELO rating, quite simple to implement), and each season the Champions League participants are the winners of each federation and the N clubs with higher ELO rating.
In the long run, this will automatically bring more clubs from the stronger leagues into the Champions League. Having also the winner of each league will allow for long-run ELO adjustment for lower leagues