@Bastien_Siebman , have you tried using the Group By due date feature on list view? It covers the functionality of auto-promotion however it’s only available on My Tasks list view. Group by exists on the Board view but does not support Due date grouping.
It will automatically create sections such as:
- Last 30 days
- Last 7 days
- Yesterday
- Today
- Tomorrow
- Next 7 days
- Next 30 days
- MONTH
Hope that helps!