As you can add a description text to suites (rich-test enabled, by the way) where you could describe the user story, this would actually work well. The only small downside I see is that things could get a bit confusing if you add a lot of test suites. The new ‘Small View’ on the overview page should help with this though. To execute all the user stories/suites at once, you could use test plans.
I haven’t really thought about such an scenario before so thanks for bringing this to our attention. I believe this wouldn’t work well with a lot of user stories for performance reasons at the moment though.
How many user stories do you plan to add?