Your system is beautiful but has one major flaw, which is causing your problem with slime in the root system. Your buckets! I noticed it back in page 5 when you where showing your root, your buckets should be solid black, but I noticed yours are green (and kind of sheer) you can see light bouncing off your reflective film THROUGH the bucket. :
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I love those buckets (I have a thing for the color green) but they have to go! Switch them out for some solid black ones. If you cant find any around just double up your buckets (let one bucket nest into the other one). I think thats why you are getting slime. I found that heat was never the cause of slime, but once you do get slime heat does nothing but help the bacteria spread and propagate quickly. Your heat should be fine. No light to the water = clean fresh water all the time
I hope this helps you man.
Ps. You look handy, I suggest you try to build an aeroponic cloner system (works wonders!).