It's not quite that simple – you are starving out
a lot more than just algae by maintaining current nutrient levels.
Starving out the algae isn't even a desirable goal in and of itself since, as you're seeing, it promotes even-worse algae that love low nutrients.
This is most-especially true about newer tanks....they need to be fed, not starved.
I would stop GFO and carbon dosing ASAP. The algae reactor is optional....it will be easier to get a handle on balancing things
without it running and I would give the most serious consideration to shutting it down for now. But I understand if you don't wanna have to restart it later. You have to make that decision. (The reactor is not helping in the short term though...you will have to work against it.) :)
Dosing the tank with what's missing (N or P; nitrates or phosphates) is the correction that needs to be made in the short term – as dictated by your test results.
Seachem and Brightwell both make fertilizer products that would be appropriate....DIY formulas exist too if you google a little.
You will like the info and links on this thread to get you started:
Dinoflagellates – Are You Tired Of Battling Altogether?