The reason you should wait until phase 2 for the anti-fungal is the die-off symptoms you will experience when you’ve been on the diet for a while. If you go on the diet, and start the anti-fungal at the same time, the intensity of the die-off symptoms would likely double at the very least. Have you already experienced a full period of the die-off?
As far as the items you named being used in phase 1 are concerned:
I took the Organic Spirulina during my phase 1, but not too much. I did have pretty bad die-off symptoms, but it was definitely tolerable, and I was actually glad to experience it because I knew what it was doing to my system. As far as the other items you’re using, I would judge that by my own reactions. If the die-off is too severe and you don’t want to experience that level of die-off, you might consider cutting back on them. That is, unless someone else has more experience with the supplements and has different information about them.