How about this: maybe instead of reordering them or deleting them, try switching just the animations by dragging them into the character's animation boxes in the order you would like them to appear in the store and then change their values accordingly. So lets say you have characters showing up as 1, 3, and 2, but you want them to show up as 1, 2, 3 in the store. Then try switching the animations and values of character 2 with character 3's. Hopefully that fixes it.
Why you dont just use "Drag" system, click and hold on your character and move it to position 2.3... i know it's working, in that way i test my characters, when i want character 2 to play, i drag character 1 down, and reorder...