Looking at the pictures, and examining the gravel sample closely, I do not think you have Black Beard/Brush Algae, or at least you don't have it by itself. (Beard and Brush are interchangeable, I prefer to say Brush because "Beard Algae" sounds gross to me, and I have a beard.) Black Algae has a limited amount of time it appears as just a spot before it grows. You haven't seen this, and it's been in my tank for a week and I have not seen it. I have seen no growth, with excess nutrients and limited filtration.

I suspect it is more a combination of Diatoms and Blue Green Cyanobacteria. The reason it appears black is due different factors, including substrate color, death, the accumulation of microscopic detritus (mostly fish poop that has been pulverized during mechanical filtration), and that there are thousands of species of Diatoms and BGC that grow in freshwater and they're hard enough to identify by themselves let alone with interaction. This, from one of your tanks, appears to be nearly entirely Diatom: https://imgur.com/PSKu1UQ
Whereas this: https://imgur.com/GMMozwm appears entirely BGC. It could be entirely BGC that appears brown as it forms new growth, but I suspect additional Diatoms because the brown color can be quite dominant on some rocks, and because the conditions for Diatom growth are nearly ideal.

IN THE WATER
High pH: adverse effects on many treatments (even bleaching the rocks, to a small degree).
High Nitrates: Offers nutrients, is part of the nutrient-light imbalance
Microscopic Detritus: Same as Nitrates, also explains greater growth near inlets.

INFO I GATHERED WHILE LOOKING INTO WAYS TO COMBAT BLACK BRUSH ALGAE (WHICH I NO LONGER THINK YOU HAVE)
Siamese Algae-Eater or Flying Fox
While the Food and Agriculture Organization has endorsed common names for these fish, use among dealers and breeders is often interchangeable. The only fish among them that reliably eats Brush Algae is Crossocheilus siamensis, "Siamese Algae-Eater". They are distinguishable from their name-competitors in that they have a clear, solid black stripe running down their side from their nose onto their tail. If the stripe stops before their tail, or there is another stripe running down their spine, it's not a Siamese Algae-Eater.

Chinese Algae-Eater
(As it turns out - I was quite surprised) Not Chinese. Rarely if ever eats algae. Prefers feeding on the slime coat of other fish, becomes aggressive when it matures, and has been known to kill entire community tanks.

Shrimp
PRO: Amano Shrimp seem to be the go-to shrimp for handling all kinds of algae, including Brush. Cherry and Ghost Shrimp as well.
CON: In the same tank with a carnivore/omnivore fish, shrimp can become fish food.