The fish above seem to not be succeptible to it, but every time I try to add a new fish, it gets sick and dies.
This happens frequently and it used to happen to me. You are correct that you have ich in your tank and it is not affecting your fish. They have become immune or undoubtably they also would be dead. But you said, they are living fine.
I believe many fish in many tanks have ich but it is not causing problems, I am certain it is in my tank but has not caused problems in many years. If I put in a new fish, it sometimes exhibits some spots, but they disappear.
I am going to say something here that everyone on here will jump on me for but it is what it is and I have been dealing with ich for over fifty years so I have a little experience with it.
"If" you want to try something before you remove all of your fish for 8 weeks (which would also probably work) try this.
Only try this if as you say your remaining fish don't show ich and you are sure your new fish are dying from ich and nothing else.
The next time you add a fish (make it a cheap fish) Quarantine it as you normally do then don't add it right into your tank but put it in a container used for livebearers or one of those hanging baskets so the fish can be easily removed, put this in your tank.
Put some rocks in there so the fish can hide. Feed this fish well with some live blackworms and maybe clams if you can get it.
If this fish gets ich in a few weeks like you say the new fish do, then remove it and treat it in copper. After two weeks put it back in the cage in your tank.
The idea is for the fish to build up an immunity from ich like the rest of your fish seem to have (and all of my fish have and many other fish in many tanks have)
We as humans get shots of various diseases to build up an immunity.
Most people will disagree with me on this but my tank has not had visable ich in about 30 years and some of the fish are 17 years old.
So if you want, just try this and I would be interested in the results.
Of course if all of your fish are dying of ich, that is another story and if your new fish are not dying from ich that is also a different story.
If your new fish are not breathing hard before they dye, they do not have ich. Spots are not the most reliable indicator as ich spots are very tiny and look more like dust.
OK have fun while I wait for everyone to yell at me.