Update of the day...
This afternoon I did something different and "popped" the white thing off of the caulastrea. It is really soft and squishy, and it's some sort of tissue, not calcification at all despite its white appearance. It is white just on the outside area so to speak, the internal parts are more pinkish/less white. It looks like a sponge to me.
The skeleton of the hammer looks a little more less green down below the area of the polyps, which is a bad sign. It might be actually dying for good, as this area was always green. I'll let it there, though. (Edit: I forgot to mention: it is not smelling bad, I finally could test it)
I read in some other site some stories about similar issues, something like a white/brown thing growing over the euphyllias in general (not just hammers) and from these descriptions it looks like this same thing happening here. Some say it could be brown jelly sometimes, but most of these episodes seem to be some sort of a sponge-like creature growing over the coral but the coral was also with problems already before the growth - not well adapted, weak, etc. so it could have also helped for these things to take over the coral.
It was also said that the Euphyllias are (maybe like Xenias) good indicators that the water quality isn't that good (ok, the tank was kinda fresh and new but the water was fine in terms of parameters until that ammonia peak...), and that it's very sensitive to chemical wars, which might have happened somehow.
A common tip was to dose/reinforce iodine, but as I've heard that it can also be toxic if overdosed, I am not sure if I should try some higher dose here, and a dip probably won't help much now.