To work better with Asana, you’d likely want to have one task per notification so you can use the Due date field with each.
To then group all those by healthcare provider you have different options so it would depend on your overall goals/workflow which is beyond the scope of this reply (I help clients with things like this daily with consulting engagements). But consider either one project or one section perh provider. Another option is using a parent task as the provider to group subtasks for each notification (you still get one Due date per subtask) but rules don’t directly work with subtasks in Asana so you could use a workaround (making them parent tasks too in this or another project) or using @Phil_Seeman’s flowsana.net.
Thanks, that is good to know on the engagements and already using @Phil_Seeman 's program - looks like a good upgrade to the current Asana based triggers.
Appears the way to handle this is to have the due-date reset when placed in a new section. Doesn’t allow time-based triggers for various values - which would be nice - but will hope to see in future.