OK, if I read you correctly, the PFA allows contact only if it's initiated by you? I would just be careful to keep the contact to the BARE minimum, and limited ONLY to communication concerning the kids. If you start getting casual and sloppy about it, he will argue at some point that you initiated the contact.
Stay on the alert. BlueSkies is right--he may be "behaving" right now and even not drinking, but the abusive personality is still there. Just be very very careful.
Glad to hear things are going well in your new space, and yeah--rent reduction is awesome!