So I feel a little stupid for only just figuring this out, but there's a way to hide the kanji stories on the front side of your card when reviewing. You can show the stories with a mouse click whenever you need it, and voila! No more nagging, 'cheating' feeling.

Here's how you do it:

Go to 'Browse'. Select your kanji deck. Click 'cards'. Assuming your fields has a 'Story' entry, add in {{hint:Story}} after any html for the 'Keyword'. If your story field is not called 'Story', but something else, enter that name instead of 'Story'.

When you review, you should see a clickable blue link that gives you the option of seeing your story or not.

Anyways, I just thought I'd post this for the less technically inclined/prone to experimenting anki users because it's not an obvious feature. Hope this helps~