Certain mites and lice do NOT feed off of the bird (bite the bird/suck blood) and therefore just won't be killed by a topical pour on product. Some eat the shedding dander or feed of the feathers. They won't be killed by the pour on products that work by absorbing into the skin/blood stream and kill parasites that bite the actual bird.
Topical products that are meant to kill by direct contact WILL kill them. Sevin dust (this is all I've ever used after the pour on products failed) will kill any of the lice/mites, biting or not. I haven't used the flea and tick products, but those should work, too, if you can get it soaked on the bird all over. I just find the sevin dust the easiest.
Nothing is likely to kill the eggs (the clumps you see on the feathers) You will need to physically remove those the best you can OR continue to treat and re-treat until all are hatched and GONE. It's possible for him to have several different kinds of mites or lice, but the ones that lay their eggs on the feather shafts live their entire lifecycle on the bird... they don't infest coops. Some only feed on the birds, but breed and hatch in the coops-- those require coops to be as thoroughly treated as the birds!