Well you should probably summarize what your current tank configuration is as well as what your current dosing scheme is so that it's clear what's going on and what changes you've implemented. For example "dosing EI" is too broad a statement. Confirm how many teaspoons of what are you dosing and how frequently? If using a solution, exactly how did you prepare it? You could have easily miscalculated the mixtures or the amounts so we need to be sure to avoid a wild goose chase.
It's a good idea to change your mindset a little. In you post you mentioned:
...my hc is doing badly, perhaps because it is getting covered in algae...
The reality is that it's just the opposite. Your plants are not doing well due to starvation and that's why they are covered in algae. Algae can be thought of in some ways as hyenas or vultures - they attack weakened or dead plant tissue. In order to stop algae therefore you must have healthy plant tissue. This can only be done by feeding them proper nutrition thereby making them strong enough to resist the hunters. You should view algae as a
symptom of weakness, in the same way that a runny nose and coughing are symptoms of the flu for example.
The other thing to keep in mind is that generally, the types of algae are indicative of which nutrients the plants are being starved of so this is why it's necessary to state your dosing quantities even at the cost of being redundant. BGA for example can be a symptom of poor nitrate levels or poor flow so you may have eliminated it by improving the nitrate dosing but I really don't know what "under control" means from your point of view. For me that would mean zero BGA with zero recurrence. If that's the case then there is no need to use the antibiotic.
The other algae sounds as if it might be diatom algae which is common in new setups especially if the lighting is high. Blackouts do help here but it will recur after the blackout if you still have high lighting. This is why we need to know what lighting configuration you've settled on. You may need to lower the light further.
We also need to know what time is lights on/off and it's relation to the CO2 on/off time. The gas should be turned on an hour or more before the lights and can also be turned off before the lights go off.
It's also not exactly clear how you improved your circulation. Did you add powerheads or did you upgrade the filter? How did you improve the distribution patterns? This is also important as you need to force CO2 enriched water down to the substrate level where the HC is located.
Cheers,