Note that the Kaf Hachayim does not claim to be explaining the Mogen Avraham, just the Rashbi.
He also doesn’t say he did it every week; in fact, he brings the Zohar as the M.A. does, that he only did it on erev Pesach.
In theory, the reason the K.H. ascribes to the Rashbi not eating shalishudis on erev Pesach should apply the whole year, yet he doesn’t claim that he did it the whole year. Presumably, even the Rashbi only relied on the “shvilei d’shmaya” sevara when he couldn’t eat pas.