These coral are very durable and so long as there is still tissue in the skeletal head, recovery of a weakened polyp is usually possible. I have had a black sun coral, in addition to an orange one for years now, that was given to me with so little tissue left that I thought it would be impossible to recover from having been ignored and not fed at a fishstore that they gave it to me because they know it was doomed there. It's now fine, though the black ones, in my experience, aren't quite as hardy as the orange or yellow ones are.
It sounds like you're doing all the right things with water quality being your first goal. But, whatever the readings are at this point...and you should continue to do the water changes, etc....IMO, you need to coax the coral into eating so that it can generate tissue and not deteriorate further. While it's generally the case that they open at night, if they become comfortable and start thriving in your reef, they will open up at any time of day, so long as they sense that there is food in the water column.
I'd start out, though, trying to coax your sun coral into eating in the evenings at first because they are most comfortable that way. There are different ways of doing this...Mine would always respond to Cyclopeeze being in the water. It doesn't matter if it's frozen or freeze-dried...once Cyclopeeze is in the water and they detect it (by some sense, maybe smell) they begin to open. Once you see the heads opening, cut off the water flow in the tank. I find that using a turkey baster to place chopped mysis shrimp and/or Cyclopeeze onto the open polyps is the best way to apply the food, which is rapidly ingested by the open polyps.
It is important to protect the coral while it is ingesting the food from fish and other creatures like shrimp that will make every effort to steal away the food before the coral has a chance to completely ingest it. You can just use the turkey baster to chase them from it or put some kind of protecting cover over it like a glass or glass jar, like blown mentioned, for a while.
Your efforts to correct all water quality problems should show good results soon, Florida, and getting food into the sun coral is very important at this stage as you know. So, try the Cyclopeeze if you can, otherwise use sometkhing like chopped mysis which it should also respond to, then use the turkey baster and you should see positive result pretty quickly.
