You cannot edit a published story. You would have to take it down again every time you wanted to make a change. Also, DO NOT DO THIS. It is a highly discouraged practice here.
You can have people test your game right now, without publishing, and without receiving backlash or poor ratings. Just keep preview mode on and then make a post in the writing workshop telling people which story you need beta read and ask for assistance and feedback.
Edit: Adding a link for your story's page or the direct link to the start of it would be wise, as convenience helps everyone.