I do think this is still one of the few things missing from Checkvist’s scheduling facilities. There is a distinction to be made in many domains between when something is due, and when it should grab a user’s attention.
I’ve used a variety of schemes to model this. The one which has stuck best has been to use a ‘start’ (or similarly named) subtask for which I set a due date. But it requires a certain discipline that a built in facility wouldn’t.
As for what exactly would work best, I’m not sure. Perhaps an additional ‘start’ date. Or maybe multiple colour-coded or annotated dates could be added to an item. Or perhaps it could be possible to associate a task with a date range (conceptualised as start → end).