Isn't it possible to add a due date for single elements of a checklist instead of a whole card? It would be very useful since within a card elements have different deadlines and priorities.
AFAIK this is not possible. One workaround for you would be to reorganize your tasks into lists instead of cards. Doing this would allow you to create a list for a particular project/task, and then use the cards and their single due-dates as the individual tasks.
This isn't the best solution, but if you would like to request due-dates for activities in a card, I suggest emailing firstname.lastname@example.org - they will have to build this in.