[mcny]

The following is very YMMV. I anal and I'm not a Google employee (would love to be though!).

For those in the US, the approach I've taken is to create a Google Voice number. Yes, you need to give it your existing phone number. Then, you can give this number as a backup but the key is to use a two step authentication app like Google authenticator or authy. This is key because like any sane system, two step by SMS has rate limits in place. I don't know the details but it seems like rate limits apply even when an SMS never leaves Google (the SMS originates at Google and ends on your Google voice with no forwarding).

Long story short, if you want to fix your problem, try to get two step authentication using an app for your account(s). I think that should do it.