(I think there's still something wrong with the "NOW" pictures.)
If you intend on corals (I think I see corals, right?), it's highly advised to raise your specific gravity to around 1.025.
Just to be clear, do you test for copper currently and find positive levels (e.g. .25 ppm) even after water changes and activated carbon treatment? (what is a carbon sheet? Activated carbon should have a sandy, gravely or pellet form.)
What copper product did you dose and what test kit are you using?
Just as a sanity check, if you test your fresh new water change water for copper, do you get a zero?
Have you tested for phosphates? If PO4 is zero-ish then your nitrates may be "high" because of that. If that's the case, then water changes may actually be hurting things rather than helping. Let us know if you can test for phosphates.
I suspect your existing fish may be immune from something they are still carriers for, such as ich.
Not a big deal, but you may have to wait for their immunity to fade (which means they finally kicked the parasite out completely) before adding new fish to the tank. This is reported to take up to six months, at least for ich.
If you're still running sub-therapeutic levels of copper (as suspected) that will be a contributing factor to the fish remaining unable to completely kick the parasite.