As has been pointed out, it's open source (specifically, Apache 2.0)[1]. So, fork the code[2], if necessary find&replace any google trademarks, and republish as a dedicated authenticator for your own app. Or use one of the existing apps which have forked off gauthenticator, e.g. https://github.com/kaie/otp-authenticator-android .
[1] Except for some bits specific to gmail's 2-factor workflow added after v2.21
[2] git clone https://code.google.com/p/google-authenticator/
Or I can implement or build from source a TFA app I trust and use that.
I really hate sites that support TFA and don't support authentication apps as I have very poor phone service at both my home and place of work and hence SMS is a frustrating experience for me.
IMO a shared-secret OTP app is certainly not unbreakable but is more secure than SMS.
SMS is known to be easily subpoenaed and universally stored while believing in a widespread OTP app trojan-horse requires some form of tinfoil-hattery. Both are still orders of magnitude more secure than single-factor authentication anyway and hence I believe both should be included in a reasonable 2-factor authentication solution.
Personally I can't adopt an SMS-only 2-factor solution due to service issues anyway.
But then what if Google pulls the rug out from under apps that rely on it and what if knowledgeable users like you don't like the idea of a third party having access to their second factor?
I'm starting to think that unless you're willing to build your own authenticator apps for multiple mobile OSes SMS-only is the best way to go.