I would first ask a question why it happens so that all stories are completed late. Is it possible that all stories need 9-10 days to be completed? If not than probably developers are focusing on starting building another story avoiding mundane task of testing.
Limiting work in progress can be something which can help to change the focus of the team. This is one of concepts of Kanban. It basically is a limit which tells you that you shouldn't have more than x stories on a specific stage.
In your case it can be not more than 6 stories being developed at the same time. Having such limit enforces people either to push stories further down the development process, e.g. start testing instead of building another story from the backlog, or help other developers to finish their stories.
To make a simple example: if every single one of your developers is developing a story and you have a limit of 6 on development stage, the situation when someone starts building a new story before the old one is finished shouldn't happen. What more, if you set one limit of 6 for both "under development" and "development done" columns your developers will have to start testing finished features in the first place before they are able to work on a new story.
Of course limit shouldn't be arbitrary set on the number of people in the team. It will vary depending on a process, team, the way you work (e.g. if you pair program you effectively have 3 "work units," not 6), etc. Try to experiment to find right limits.