Wow, sounds like you're serious about this with all of the manual work and the CUC that you ordered.
Let me see if I can tie all of this together for you so that you've a coordinated strategy going forward.
Almost all "dead rock" has the potential to have absorbed phosphates, either in the form of precipitated calcium phosphate on the surface, or in the composition of the rock itself if it's man-made; one of the biggest uses for recycled phosphorus from fluorescent bulbs is as an additive for cement and concrete. Algae is capable of extracting this phosphate from the rock to use for growth, so the water concentration of phosphate can be zero or nearly zero and the rock will still support luxuriant algae growth.
Very little phosphate is required to support algal growth - just a few tens of parts per billion is enough. This is well below the limit of detection for all but photometer-based ultra low range test kits. This is why the Hanna Checker Low Range (713) and ultra low range (736) tests are so popular. These tests allow reefers to sensitively measure the phosphorus/phosphate concentration in the water and determine when a chemical filtration means like Granular Ferric Oxide (GFO) needs to be changed.
The species of algae matters. GHA like derbesia and related genuses typically do respond to nutrient export from the tank and good husbandry practices. Bryposis, however, is known to be problematic regardless of how low the nutrients are in the tank. And almost all creatures will refuse to eat it. That's where the TechM technique comes in. Bryopsis is sensitive to a contaminant in TechM, though not the dominant material (magnesium). Typically, one needs to raise the mg concentration of the tank water from perhaps 1200 ppm to at least 1500 ppm with TechM to get enough of the contaminant in the tank to be effective. For a 210 gallon, this is going to be quite a lot of TechM - roughly 2 liters. So if you decide to go this route, buy a gallon size.
A warning about TechM treatment for bryopsis - adding this material in large quantities to a tank typically wipes out the shrimp and snail population, though some species seem more resiliant than others. If you algae is indeed bryposis, you should see an effect within 3-4 days of adding the TechM. If it responds, you should maintain the TechM additions (with water changes to remove the excess magnesium) for 3-4 weeks to totally wipe out the bryopsis and ensure that it won't return.
With respect to nutrient export, it's essential to have a good skimmer and use effective chemical filtration (typically, GFO and GAC). If the rock is actually leaching phophates, that reservoir will eventually be depleted, but it will take a few months with diligent chemical phosphate removal. That can be quite a lot of GFO, which is expensive. You may want to consider regenerating your GFO, which can be done with a sodium hydroxide solution in a mason jar on the kitchen counter.
With respect to "hurrying up" the depletion of a phosphate reservoir on the surface of the rock, you can consider acid-washing. Given that your tank's already set up with inhabitants, this would have to be a one-rock-at-a-time procedure. The basics are removing a rock, rinsing it off, placing it in a plastic bucket/tank outside, and adding diluted muriatic acid (muriatic is the common name for HCl, btw). The muriatic acid will react with the calcium carbonate on the surface of the rock, dissolving it. In the process, it will also dissolve any precipitated calcium phosphate. Then you thoroughly rinse the rock and place it back in the tank. You'll need to wait a week or two to treat the next rock so that bacteria have a chance to re-populate the treated substrate and you don't wind up wiping out your entire bio-filter by doing all of the rock at once.
Note that if your rock is man-made, the acid treatment may actually make things worse if the rock was made with typically cement products that contain phosphorus. Since the phosphorus would be throughout the rock, the acid treatment would just expose more phosphorus-rich surface area to leach into the tank.
Finally, if your tank is a Fish Only with Live Rock set-up (i.e., no corals and no plans for corals), I think most of us would suggest that you simply live with some algae. The fish don't care, and it can be a whole lot of work and expense to control algae in a setting where it doesn't cause any harm.