The September, October, November schedule has existed for decades at this point, i'm not sure why people every single year seem to think the international break is increasing. There actually used to be more international breaks. Up to about a decade ago there used to be an August game also, and previously February and April had games. The international game has already been consolidated, though two of the Autumn breaks will be merged going forward. At any rate the reason the club game extends later in the season for premier league clubs nowadays is due to increases in European games, not international games.
England are also not the only team to play international games. Most these "solutions" are always very England-centric. May isn't the end of the season for many leagues around the world, and strangely enough every country has an international team.