Let's say qualification was part of the playoffs at the end of the previous season, and then the teams that qualifies would have to designate a 15-player roster for the entire tournament. The players would be given a no-cut, no-trade contract for the length of the tournament. Only players on the 15-player roster would be eligible for play. They could be used for league, national cup, and scrimmages
Or teams in the international cup could be excused from early rounds of their national cup - so they would still be playing 3 games per week. Once they were eliminated from the international cup, they would switch back to their national cup.