One thing I've noticed while playing vs Eddie is that Anji's air-to-ground can't really compete with Eddie's various forms of anti-air, most of which leave you on the ground ready to die.
Another thing is that it's often difficult (for me at least) to hit Eddie out of his jumping kick, so I prefer to guard point it, as it can be extremely predictable. The only problem I've found with that is the occasional random gallery.
I've also tried to move away from 6HS, broken as it may be, as much as possible and replace it with other guards, since whiffing or getting blocked while using that move is practically a death sentence against certain characters. I (and surely most Anji players) have noticed people clearly attempting to bait and punish 6HS and in my experience using a different guard with less cooldown often leaves you at a neutral point if they don't follow through, or with them up in the air eating Kou or whatnot if they do.
Same deal with Kai imo. I often only use K Kai when I have the tension for RC or after huge, confusing blockstrings because the cooldown is just too huge otherwise.
Anyway, as was previously mentioned, Eddie is lacking an efficient way of getting out of pressure, so it's a matchup that often goes to whoever knocks who down first/the most. Knock him down and then stay on him like a maddened, fan-wielding animal.