Ok that all makes sense.....corals, algae and many other microbes in the tank all need these basic nutrients.
No nutrients and those things all have problems. Some will even die off.
I wouldn't bother running this reactor for a while – at least until the tank stabilizes and has
continuously positive nutrients for a while. The object is for it to use "excess" nutrients – and so far you do not have excess nutrients.
How are they doing in general? As long as they're not sick or languishing (ie. they are moving around and eating
something) that probably just means you still need more herbivore snails.
Have you tried tweezers or any alternate ways of plucking the algae with your fingers? These algae usually have a "root" or "trunk" that you can pull and get 90-100% of it. It seems like it's slow-going, but pulling this way is pretty permanent. If you can hit the tank a few times in a row without letting a lot of time pass in between, you can make progress.
Snails will keep those areas clear if you have enough of them.
Use this to help your progress as well:
Algae Cure!! Spot Treating Algae With Peroxide
Seachem or Brightwell (and I'm sure others) make fertilizers. I'd probably say get both some nitrate and phosphate to have on hand. You're just going to dose long enough for the tank to start maturing....and so you don't have zero phosphates again while the tank finishes maturing.
Save the reactor for sometime down the road when you need it – just leave it offline/empty for now.
Phosguard is made for removing the nutrients we're talking about dosing, and the carbon is just not needed.
Starting up that reactor would stall your tank even longer, possibly even promote a worse algae in the process. We're trying to do the opposite – get it moving forward
past the algae stage.