Hi,
I like to first wait and see what the moderator says... but here I go anyways.
The thing I notice first off is that you have a 250 watt MH light on a fairly small tank. That's a lot for a newly shipped specimen, so I hope you put it in a shady area off to the side.
It would have been better if you had acclimated it in a separate quarantine tank to see if problems like this were present as some can be contagious-there could be infections, snails that eat zoas, nudibranchs you can barely see that will spread to your other colonies which can also arrive as eggs, and dead zoas are pretty toxic... and it's possible that a new problem will arise noone has heard of before. Seems like we get a new one every other year that devastates tanks. If you have the ability I would move it to a separate tank immediately after taking a few steps.
Set up a strong light on a desk protected by a layer of newspaper with white paper towel over it to make visibility better... Use gloves as some zoas are very toxic and it's hard to know which are which. If you are worried protect the desk further with a hefty steelsack or something disposable. A magnifying glass is helpful, and a freshwater dip should be on hand with a timer. The dip will be matched in temp and ph to your main tank, as will the quarantine tank. Other tools I like are bamboo skewers and a boars bristle paintbrush about 1 cm wide tops, new and stiff but not as harsh as a toothbrush. A container of tank water and turkey baster are also useful for rinsing loose stuff off.
Examine the zoas carefully, they can be out of water for a while so don't worry... Take a bamboo skewer or other thin but not too sharp tool to lift any loose zoas. You are looking for eggs of nudibranchs, actual nudis, snails and sponge. The sponge usually dies in shipping and rots, looking and smelling aweful. Actually a sniff test is really quite helpful
Remove anything loose and rinse it off into the tank water for later examination. Nudi eggs look like little white spirals, I think... someone want to help on this? I have never seen them. Reef spiders are a pain, they eat holes in the zoas and are very hard to see/remove. They looked like a hair wrapped around the base, they are that thin. Anything at all that is not zoanthids pry it off with the skewer. If necessary you may have to break the rock up, sometimes there are other coral on it that you want to save but they are stinging your zoas. I had a brain coral on the bottom of my orange zo's and had to chisel it off because it was stinging them to death at night.
Next I do a 3 minute dip in freshwater and use a boars bristle paintbrush to scrub them off while they are in the water, getting between the polyps and in crevises wherever possible to remove everything loose. After the timer goes off swirl and put in the quarantine tank. Hopefully this will do the trick.
What else... There are various dip formulas out there but right now I think we need to know more about your situation. Like does it stink? Then it's probably just rotting sponge. Was it put right under the halide? Likely light shock is burning the zoas and weakening them. Did you find any predators on it? Or maybe one side of the colony got smashed in shipping and the zoas are damaged. I don't know what you do for that.
One time I dipped in chlorhexidine and got excellent results but I don't remember the dosage. Perhaps our moderator knows of this? It's antibacterial, usually used in mouthwash, or for surgical scrubbing. Livestock people may use it in animals' drinking water to keep it sanitary, but you are not supposed to drink it. There is an old school dip of potassium permanganate but I don't know much about that, my friend uses it and then neutralizes with hydrogen peroxide. Stuff is toxic as hell and highly staining. Does kill anything in the water though, and Kent still sells it in a couple forms. Anyone ever use that for zoanthid problems?
Kate