Is there a way to sign in to Apple TV on Fire Stick if the QR Code doesn’t come up?

My question is this: In the absence of a QR code, is there a way for me to actually sign in to the Apple TV app on a Fire Stick device? Details are below. 

I have seen many, many articles on this over the last year, but no solutions. I have THREE Amazon Fire Stick devices. I bought them all at the same time and installed them on three similar TVs last week. I attempted to install the Apple TV app on all three.

On two of the devices, I installed the app, opened the app, and a QR code popped up. I scanned the QR code, followed the link, and the app works perfectly on those two TVs.

On the third device, I installed the Apple TV app, opened the app, and there was no QR code. There were just two buttons: “Sign in Later” and “Sign In or Create Apple ID.” I clicked on the second button, entered my credentials, and got a “verification failed. Try again in a bit” error (I don’t remember the exact wording, but that was the gist).

I have tried this approximately 25 times over the last five days. 

I came to the internet 5 days ago and learned that the “verification failed” error is due to Apple’s 2FA and that it’s not going to work regardless of how often I try and that I probably needed to update my Fire Stick device. I did that. Uninstalled and reinstalled the app. Still no QR code.

I’ve even tried checking for new updates about six or eight times since then even thought it says it’s up to date. Uninstalled and reinstalled the app again a few times. Still no QR code.

It’s updated to the same settings at the other two devices that loaded with QR codes. But still no QR code on this device.

I have since then tried every combination of restarts, powering down, etc., and have even done a factory reset twice. This one Fire Stick device will not load the app with the QR code for me to sign in.

So again, my question is this: In the absence of a QR code, is there a way for me to actually sign in to this app? 

On a whim, I tried going into the Internet app on the Fire Stick device and going to tv.apple.com. I can sign in there without any problems (though I cannot access my purchased content in my library this way, so it’s no help). It makes the 6-digit code pop up on my phone and I can enter it and that’s fine. But then the app itself still is not signed in and even if I stay signed in in the Internet app, I cannot sign in through the app.

Amazon has tried to help me for hours — I’ve talked to eight different people — and they suggested I ask Apple if there is a different way to successfully log into the app if the QR code doesn’t work.

(Note that all other apps work on this particular device. Netflix, ESPN, Hulu, etc., they all gave me QR codes on this device. ONLY the Apple TV app won’t give me a QR code.)