Best method to solve this would be to create two custom fields on the screen where you are printing this report from, do it in the same area of the screen where the start and end dates marked in yellow are getting their dates from. Seems like it would be the header in this case.

Create a read only custom field that has a select statement which joins to the view where the green start date or end date columns are, and use the min or max function to get the correct date. 

Once you have added the custom field and it shows on the screen, you should be able to reopen report designer and see the new custom fields in there somewhere in one of the folders on the left side. Then swap them out on the report header instead of the existing column values.