A general Summer release date sounds reasonable to me. Or early Fall, I guess. I think if it was going to be Spring, we would know by now.
I still have a gut feeling that our friend Mr. Ponytail from Badlands is going to feature in at least one of the shorts from the animated film, so I can see them really wanting to go right from one to the other to bank on that synergy (like how "Final Flight of the Osiris" in The Animatrix leads directly into The Matrix Reloaded, and how "Kid's Story" sets up a character that is then seen in Reloaded and The Matrix Revolutions.).