I really have looked for a solution for this and haven't found it.

I understand that party order doesn't matter in MM6, but I would still like to be able to switch two character's (left to right) order. I read somewhere to hold down the Ctrl key, but that isn't working for me.

Is it possible to change order in 6? Thanks!

in order to change your characters you need to select one then while holding the Ctrl Key select the other.