I don't think anyone knows for sure about the cut-off date for 1st half of the year versus 2nd half of the year challenges, but I have frequently heard starting on June 16th or later to get status until the next year + 1. If you finish by June 1st, that means you could have started in March, and I really don't think they give you a year + 1 for that.

JuileAA, if you have already booked, your best bet is to call AA directly and ask a reservations agent what your booking class is.