All the Tests are over by early January. Most Australians would consider january to be the peak summer month, and yet all they have in this time is a non stop diet of jamodi's from early january to mid february. Australia, like England, still consider Test Cricket to be the pinnacle of the game, and yet they are deprived of it during the peak summer period.
This is how I think it should be-
Play a 5 game jamodi series against one particular team starting in mid november. Then have the first 3 Test series of the summer against that same team starting in early december, and finishing in early january. Then play the next lot of 5 jamodi's against another team in early to mid january, with the second 3 Test series starting in Adelaide over the Australia day weekend and finishing in mid february, or if its a World Cup year, swap the Test and jamodi schedules around for the second half of the summer.
When England or the Windies tour for a 5 test series, play Bangladesh and (If they are re-admitted) Zimbabwe in a 2 Test series and 3 jamodi series at Darwin and Cairns in mid to late october.