Task board - add the project context to the url

Use case:
We have a browser session open with a tab for each project context, this is saved as a browser session. When reopened the project context defaults to the last project context selected, in this case one is left with a bunch of open tabs for the same assignee. If one uses a tab reloader when each tab is activated then the project context just keeps bouncing to the last selected on a tab.

Can the web service be updated to include an project context reference in the URL to avoids this happening?

I made a similar request to have the assignee added to the url GHS-3293