Two things. First, by "leech" into the water column I mean the nutrients get into the upper water column which can feed algae. I do not know how Flourish Tabs are manufactured to prevent this but they do seem to not do it. So algae is not being fed. What you describe is something else, and will occur with any substrate tab/pellet fertilizer. Never disturb these, push them down and leave them.
Second, dirt is one of your problems here. The organics in dirt is what is feeding your cyanobacteria, and the algae. The other issues like light and such are still part of the equation, but dirt is certainly a major factor.
Pleco are notorious waste factories, and this is not what you want with everything else. Snails would be a better option; they graze all surfaces eating algae (not "problem" but common) and many fish will pick at the biofilm.