This is a strange checklist you used. I don't know where you found it as it is not the one we usually have here.
Can you please let us know what exactly you're feeding? Is it a scratch mix (grains only) or a mash or a pellet? I couldn't really gather it from your answer.
Secondly, I'd probably worm them again but use a different wormer as Piperazine does not treat all kind of internal parasites. Get Avitrol plus, Wormout or Moxidectin plus. You can get them from most produce stores, some pet shops, avian vets or from online shops.
Have another look to check whether all external parasites are gone and treat them again after about 10 days after the first treatment to get any lice/mites that have hatched from eggs in the meantime. You should also clean out the henhouse and burn or bag and discard all the litter, spray it with a permethrin spray and put in fresh litter if you want to avoid them getting lice and/or mites again within a very short time.
Separate any sick birds from the other birds. It's easier to treat or observe a separated bird and you might avoid any infection of other birds that hasn't happened yet. It's a bit hard to say what is going on here but it seems that your birds have had an underlying disease for a while when you got them as they are so emaciated. I doubt it is coccidiosis as it usually affects younger birds only, although it can make a bird the age of yours quite sick if their immune system has been compromised already considerably.
Is the second sick bird very emaciated as well? If so, you might lose it too but you could try beefing it up with excellent feed, avian vitamins in the water and possibly the Rickets diet
ETA: Ah, Mike has answered in the meantime. I'll post my reply anyway.