I agree, the red film 100% is cyanobacteria. I suspected as much from your high nitrate numbers. I'm actually surprised some of your fish will eat it, I haven't found one to do that yet.
Well my battle with red slime was epic. I eventually won but what a long and painful fight. Here is my experience:
1. Antibiotics like "Slime Away" are usually pushed by LFS's but will work only once or twice before the bacteria become resistent. You just add to the number of drug resistent superbugs. The antibiotic used is usually erythromycin and is usefull in treatment of human bacterial infections but not for long if it becomes ubiquitous in the enviornment. Cool aside, erythromycin can turn body fluids like tears orange.
2. Shorten the photoperiod. I've heard of good results but in my experience, the slime tended to thin out only until the light returned to normal and there were days I did not allow the lights to turn on at all.
3. Direct siphoning. This is a very helpful method to reduce the load but not usually effective for complete removal in my experience. You can suck all you want but the individuals are microscopic and some is always left in the system and often bloom in a couple days apparently due to less competition.
4. Increase water changes. Most commonly recommended option but I had no success with it. It would get better and then return to the status quo.
5. Potassium Permanganate.
Should be used only in expert hands as there is significant risk pf toxicity if overdosed. Strong oxidizer that helps decreased disolved carbon (organic compunds) in water. Most products geared towards freshwater but there a few for saltwater systems. This significantly decr4eased my red slime load but inhabitants did not look happy about it and when I slowed its use, red slime started to slowly come back.
6. Micron
sock. I use a 25 micron sock. Only works if you change the sock often, otherwise waste just rots in the sock and stays in the system. Ultimately, this method along with regular water changes worked for me.
Red slime eating organisms are unreliable in my experience. Small hermit crabs and snails never seemed to consume enough to be useful despite various advertisements.
Perhaps you will find this useful. It represents my personal experience. Nice corraline alage growth in the photos.