The way to achieve this is not all that different from the calculated column approach, but it requires a separate table to model the many-to-many relationship between all the required relative period selections and the dates in them, as well as the use of bidirectional cross-filtering between tables (which I blogged about here). The data model I used for this report looks like this
Be sure to read the comments to make sure you don’t get into a scenario in which a user can select multiple periods and get duplicated data.