As someone who has fought BGA for months and months and months before getting rid of it (no offence to Liz and Ian, but they haven't), let me say this.
1, Blackouts won't work on their own on a heavy outbreak. Trust me. I tried it. I tried it repeatedly. I did little ones. I did week long ones. I did two 4 day ones with a water change inbetween. They did not work on their own. If your outbreak is as heavy as you claim, then it's unlikely you will be able to beat it with blackouts alone.
2. Dosing EI helps. BGA is more likely to get a hold in a tank with low nitrate because it can fix it's own nitrogen so when other plants are struggling with low nitrates BGA can still flourish. Obviously having higher plants helps as well.
3. Circulation, circulation, circulation. You need flow. And lots of it. I used a spray bar. It worked wonders. To the point where after I took it out, a small amount of BGA returned, but it never got out of control again.
4. I never tried abx. We can't get them in the UK for tanks. So I've no experience with them. However, I am a great believer in not using meds if you don't have to. So my personal preference would be to try everything else first, and then only use abx as a last resort. I would actually buy a whole new tank and transfer the fish into that before buying abx.
Is it both tanks or just one? Could you, for example, put all the fry in with their parents, remove everything from the other tank, scrub decor with a bleach solution and replace the substrate, then put all the fish in that tank and do the same with the other?
Honestly not offended. And I reiterate, a lot of people don't by into the flow theory, but as someone who never seems to get BGA, I can say that the biggest common denominator in all of my systems has been copious amounts of flow. I agree with Caz, don't do the meds until as a last resort.
L