Moving it might be a good idea although not directly in front of a powerhead. You may also need to step up the total tank flow some. The accumulation of debris, algaes and such would indicate a dead spot or it's just in need a positioning tweek/angling.
As far as the affected area, syphon off the cyano
and very very carefully/gentley use a new soft bristled toothbrush to remove the hair algae. If you can get your figers in there without breaking the coral yank some out first. Don't rub hard, just enough to pull the longer strands free. Once repositioned to get a bit more light and flow (nothing extreme), the algae should abate.
The monti should eventually grow over the dead area and look as good as new.
How's the water parameters?