There is no way to move newly assigned tasks that are due in more than a week to the later section. The addition of a greater than or lower than could greatly improve the rules in My Tasks.
Also it it counter intuitive to set a rule that include all the due date to be move to the upcoming section. To do that, I add to set a rule using OR for less than a week, due in 6 days, due in 5 days, due in 4 days, due in 3 days, due in 2 days or due in 1 day to reproduce the older auto promote in the upcoming section.
Also having a trigger that could use the start date could be really useful.
Is there any plan to develop this?