There is a chance that after the third Fire IV cast and in between the fire 3 proc, in the middle of your convert and swiftcast you can get to a point where your astral fire drops off and you get a small tic of mp. When this happens the rotation works out fine. Lucky for me I found this happened to Aikaal and you can see it demonstrated in his video at this timestamp:
Clicky here. If you look just before he uses convert you will notice he gets a small MP tic after AF3 wears off moving him from 2167MP to 2394MP before his convert goes off which brings him to 5801MP. If you get this small tic as well, which is definitely NOT guaranteed, you'll be fine. If you don't you simply won't have enough MP to cast blizzard III and will most certainly lose enochian.