Automation - has anyone done this or something similar? In googling, it appears like it is possible. We will start to look into this tonight. So thought I'd check if anyone else has ventured here... 
Epic has T-shirt size
We automatically create BRD user story based on adding component to Epic
When we create this user story through automation, we want to populate target start and target end date based on some logic.
For example, we predefine:
BRD story length of time is 14 days if the parent Epic Tshirt size is Small
BRD story length of time is 28 days if Epic Tshirt size is Medium
Target Start date of BRD story is 5 days after it's creation date or 5 days after today's date -(when it's created)
Target End date of story is Creation date + 5 + 14 days
or Target End date is Target Start + 14 days.
If it is too complicated or not feasible to do the logic for target start and target end dates during the story creation automation process....
A second option would be to trigger the target dates when the story is moved into status "Business Review" (or when story is Assigned)
So that would be... upon status change to Business Review or Story assigned, update target start and target end dates according to logic.