plate coral issue

I would not do that. Iodine is not going to kill the hair algae.
This is not uncommon at all.
I see more algae on the sand. You have been feeding too much and don't have enough herbivores. Something caused the flesh of the Fungia to recede in those spots allowing algae to get a foothold.
You could do some fine surgery and scrap the algae off the skeleton.
OR- get a few Hermit crabs with nothing else to eat. Take them from your tank. Leave the hermits in a shallow container of tank water for a day, then place the Fungia in with one edge touching the wall of the container. As the hungry hermits walk around the perimeter they will climb up onto the Fungia and, hopefully, eat the algae. 

Well, anytime I see Cyano on the sand it makes me wonder if there is simply not enough biofiltration in that system.

It wouldn't make sense to feed much less than twice/week, but an evaluation of the way the tank eats nutrients is certainly needed.
The hair algae will probably continue to grow there unless it is removed by you or some animal.

You are correct that too much stuff covering the sandbed is a contributing factor to reduced biofiltration. It's a good idea to keep at least 75% of the sand bed clear, with good channels of water flow.

Water flow is critical to helping the sand bed to do it's job. My little 12 gal Nano has only a single Rio 600 sitting on the sand shooting water almost straight up to the surface. Some hobbyists may not realize it but that's good flow. The SPS are all doing well and the RBTA is growing larger every day.