D.M.
Hi Lady---Maybe you could start with a save-the-date phone call a month in advance then follow with the formal invitation 2+ weeks before the date. Yes, it is unfortunate that people won't rsvp as requested. I don't know if it's that they're too busy or just don't want to commit in case something more important comes along. In any case, it's downright rude.
Good luck, have fun and Happy Birthday to all! D.