In each one of my PCs and also on my key-ring is how I do it.

If you sign up using one key, do the other keys work with that account? Unless it does, you're greatly increasing the complexity of creating new accounts anywhere.

That's basically what I'm getting at. Do I need to do significant amounts of extra work to keep an off-site backup in another state?

I don't personally consider it greatly increasing complexity. At account creation I register the Yubikeys at the PC and on my keyring. When I first login from a different PC I use the Yubikey from my keyring to login and then register the Yubikey at this new PC.

Sounds miserable compared to using a password manager.

Sounds like we should be doing FIDO with TPM then.

Next to your birth certificate