Actually, I have figured out my tank doesn't have Black Algae, but a form of red algae that is...well, black!
So that explains why none of those methods worked for me! I thought I was doing something wrong.
I had to take the whole tank down again, but this time I soaked the plants in a 19 part to 1 part bleach solution. 2 minutes for the more fragile, thinner leaved plants, and 4 minutes for the Anubias, Crypts, Jave Fern...etc. The hardier plants. Make sure you have a bucket of clean water nearby, so you can dunk them in there, once you are done. Then, you can scrub the little spores off with your fingernail. After that, I soaked the filter, heater, and rocks in a 25% bleach solution, for about 10 minutes, then rinsed them in clean water. I used a clean brush, to clean off these things. Then I left everything out but the plants to dry in the sun for a while. Some of the things I can't put back in yet, such as a few of the poris rocks, because you can still smell the bleach on them. I'll be rinsing those for a while.

I decided to just take out all the sand, as it was covered in algae. I have some other, brand new gravel I can put in. Oh...and if you have wood...don't soak it. It is pretty much impossible to get the bleach off, and it makes your wood a MUCH lighter color. It does look pretty natural though. Like sun-bleached driftwood.
If you don't feel like doing that quite yet, True Siamese Algae Eaters (Not to be confused with Chinese Algae Eaters) are supposed to be able to eat it. However, they get biggish (5-6"), and can be territorial with their own kind. So you either have to get one, or a big group. (5+) And a 6" fish, may not be suitable for most tanks...
Just something to add.. a fish or a plant from a fish store can bring this into your aquarium. So, I will now be soaking any new plant I have in the 19 part to 1 part bleach solution before they go in my tank. Don't want to battle this algae anymore! And of course...all fish will be quarantined. But they would be anyway!
Anyhoo, if it DOES come back...I'm going to try treating the tank with copper for a week or so, and see if that does anything. That will be my last, drastic measure. But it won't come back...I hope.
I'm sure you all are bored by now, but I just figured I'd say this, so it might be able to help somebody later on!