This is my nightmare. This is why I refuse to use 2FA. (Except on services that require it, and I wish they didn't require it.) Am I worried about getting hacked? Absolutely! But when I weigh the likelihood of (1) someone else getting into my account without 2FA and (2) locking myself out of my own account with 2FA, the latter seems much more likely! I understand how backup codes work. I promise you I will loose them…
Not all 2FA is the same. SMS 2FA leads to these problems. But A FIDO2/WebAuthn token (yubikey or similar) would help you stay secure and independent from your phone. I agree that yubikey is a bit expensive, but there are alternatives. Token2 seems quite bit cheaper, but depends on shipping: https://www.token2.com/shop/product/token2-t2f2-fido2-and-u2...
Just stick your 2FAs in your password manager, like I do with Bitwarden. I secure it with a Yubikey, but if I lost my house, I would just remove 2FA from it. My bigger concern would be to get cut out, than people somehow guessing my master password.
SMS 2FA is always a terrible idea, homeless or not. It's honestly better to just go 1FA in that case.