Good job using media from an established filter! Good circulation inside the tank ... excellent.
Maybe you can add something like Seachem Excel (glutaraldehyde) .. a CO2 supplument. Your substrate is rich in micro nutrients so don't add Seachem Flourish Comprehensive only which a lot of ppl do. It's almost entirely a micro nutrient supplement and has no macro nutrients in amounts that matter. Aside from Excel, you could add Seachem Flourish Potassium and 1/4 dose of Seachem Flourish Comprehensive.
I agree ... spot treatment with 3% hydrogen peroxide will knock the hair algae back. It won't kill the spores but under the right conditions it won't grow anyway. Make sure you leave the filter running and have some surface agitation when treating with H202. You can use a pipette or syringe to add the H2O2 directly onto the hair algae. I'll have to check the max dose unless someone else knows from memory. This is the 3% hydrogen peroxide found in pharmacies and some supermarkets. I'll post the dosage later but it'll probably be tomorrow.
Do I need to spot dose? Or can I just figure out how much to add to the whole tank? It's quite literally everywhere