Personally, I would move the ASG to Saturday so that it falls between the end of interconference play and the start of the 2nd round of intraconference play, and eliminate the double cup round. In countries with 5 divisions, I would move the cup final to the Sunday following the last regular season game. Since only two teams would be involved, this would greatly reduce the confusion that occurs at the ASG.
A 6th division already exists in Spain and Italy (but it is only twice the size of the 5th division).
As I proposed earlier, I don't think that any 6th division teams should participate in the cup. Instead, teams would play in a 6th division cup, which might also serve as a qualifier to the national cup the following season. For example, the 1024 teams that advance 3 rounds might qualify, regardless whether or not they promote to D.V.