Actually I have the AK120 and even in its case, it will fit into the AKR01 case. It's a tight squeeze but it goes in the top. I've taken the foam out of the bottom of the case and just put the headphones in there, below the AK120.
By the way, the sound of this combo is just unbelievable. You have to get a good seal on the AKR01's but once you do, the detail and airiness is unmatched. They easily outperform by IE8's and HD25I-II's (both of which I love) and come close to my Stax. I'm really looking forward to trying so of the higher priced FAD's as these are just great!