Ok, please don't take this the wrong way, but you guys don't seem to know enough about security to be running this kind of service. Being able to access your MFA token from multiple devices defeats the purpose of it being a second factor (since it's must exist only in a single place to be "something you have"), and now you're recommending a backup passcode with less security than WPA2 - a passcode to a backup that by definition should not be allowed to exist.

It's bad enough that Google's TOTP keys are too short (80 bits, below the required 128 and recommended 160+), especially given the clarity of the spec and the size of their organization, nevermind being the first large-scale rollout. It's also unfortunate that they half-assed their Authenticator app, which hasn't seen an update in over two years. At least they've had the good sense to improve the workflow of regenerating a token for a new device.

I appreciate the problem you're trying to solve and am aware that there tends to be a lot of headache in additional security, but doing this kind of thing provides a false sense of security if not outright lowering the security of what already existed. If I can get access to my MFA tokens by typing in a password, then it's a knowledge factor and not a possession factor. That's one-factor auth with two passwords, like the "security" questions on many banks.