In your stated situation, I'd just add a paragraph of two to your storygame's description with an "Edit" in front of it. There'd be something like, "Thank you, Mizal, as well for your informative review. I fixed the problems you mentioned." ( <- I did that thing on my first storygame.)
I think admins can "reset" the original publishing dates since I'm fairly certain Alex did that with Eternal the first time I took it down and republished it later with an addition.
When you're messing around with the admin functions of a story, along with the title, category, etc. a publishing date is listed and underneath a warning that, it says "do not set before xx/xx/xx" along with the exact time. That I assume was the original publishing date.
So for Eternal it says do not set before 9/28/2011 4:41:57 PM, though the current published date listed is 12/31/2013 3:46:45 AM.
EDIT: I see the story you're talking about is The Quick Dating Game. We could reset it if you want.
I say just show both the original publication date and the latest republication date.