It would be my guess that whatever particular strain of mold your child is infected by can be killed off by the keto, and not by the others. Dr. Sidney Baker talks about "the antifungal parade" he puts kids (and adults) on; very often the first few antifungals he tries do nothing and then they hit the jackpot with the next one they try.
Molds and yeasts are like bacteria--there are many kinds of bacteria, and each kind requires a specific antibiotic to kill it off. My son would do like four rounds of antibiotics sometimes for ear infections before they found an antibiotic that would work for him.

Yeast/mold is like that; one antifungal will do nothing, but another might.
I STRONGLY SUGGEST YOU GET YOUR DOCTOR TO FIGURE OUT WHAT MOLD YOU'RE DEALING WITH. And that you do more keto, and figure out how to manage the stomach upset. Dr. Baker will do a few weeks at normal dose, and then double the dose for a week or something like that--more is better, he says, when it comes to antifungals.
I am so pushy about all this mold stuff because when my son was about 6, we did a round or two of diflucan and he was a different kid!! And then the doctor stopped, and he slowly slipped back into his old, autistic self. But I did not know enough to know why. It took YEARS for me to figure it out. This "do a round of antifungals and quit" mentality that the DANs seem to have is wrong. Look at toxic mold sites; they will give better direction on what to do. Look at Doug Kauffman's books and website; also Andrea Fabry has a site that's good with good pointers. Her site's s bit scary, though, as they had a worst-case scenario and did some drastic things to fix it.
Dr. Sidney Baker has a book called, "Detoxification and Healing" that is really good.
You are right to chase after this as your core issue--I, too, got a normal child back with the antifungals and I wish, wish, wish I had known that that was my core problem and to hit that hard. We mushed around with all sorts of things before we got back to that.
The Feast Without Yeast diet was BIG for us. GAPS seems to be great for some, and the Body Ecology diet, if you can do it, is really great too. The "standard" "mold" diet is basically the SCD, but they work into allowing grains after a couple of months of detox, which the SCD does not. All these diets I just mentioned are very similar but have their own twists in that some allow grains, some no meat, some balance the two....I think they will all "work" and that the trick is to choose the one that best fits your child and has food that he will eat.
You are very perceptive to suspect mold as a core issue! Good job, mom!!