Google Authenticator passwords duplicated somewhere else?
So I dug a little deeper. This, however, requires I disable and remove the current 2FA from my account.

Go disable/remove current 2FA
Go enable it again, but remember to grab the secret (it's listed somewhere in the request or on the page) and save it somewhere
Find any secret -> One time password "generator"

Now I have the secrets synced on my PC and on my phone. Pretty neat. Requires a lot of work, as I need to disable all my authenticators, but it does work actually.
I'm trying to know if this is possible at all. So far it doesn't look that great. Let's imagine I wanted to list all my current Google Authenticator passwords somewhere. That list would update once there's a new set. Is this possible at all?
I remember back when Blizzard made their authenticator. You would basically have to enter the recovery key/password from their app into a program, which could then show your authenticator on the screen and on your phone or physical device (yeah they sold those). I imagine they used TOTP just like Google Authenticator does. 
So my real question is: I have my x amount of Google Authenticator passwords, which refreshes every 30 seconds. Can I pull these out and show them in another program? Java? Python? Anything? I assume "reverse engineering the algorithm" and brute forcing the keys (like grab 100 keys and work out the next key) would be impossible, as these are server-client based.. right?