I do not remember "evidence that any of this stuff really works" about curing an existing cancer, but there was rather strong evidence in large-scale studies with various lab animals, in which a mutagen agent created tumors when they were fed normally, but no tumors appeared when they were malnourished, either by eating a reduced amount of protein, or by eating the normal amount of protein, but with a bad amino-acid profile.

Both forms of malnutrition would diminish the capacity of synthesizing proteins, which would affect mainly a fast-growing organ, like the tumors. Presumably this slowed down the growth of the tumors, allowing time for the immune system to react and suppress them in their incipient form.

Unfortunately, malnutrition as a prophylactic measure does not really work, as it enhances the risk of other diseases, even if it might lower the risk of cancer.

The method described in the parent article might have better chances, but it seems likely to work only with a cancer that has been discovered very early.