I tried my Mini in my LTD Koa 12-Fret case. It fits! Neck supported properly; maybe a little bit of padding at the pin end is all that's needed. Now, I don't think I will use it for travel, because it's a nice case and my Koa needs it!
I'm thinking now I'll look for a 12-Fret GS case. Don't tell me I don't need one! I want one!