I'm confused as to why you'd need a third-party for this.
Example of how to generate a seed and share it with an ssh server: https://scottlinux.com/2013/06/02/use-google-authenticator-f...
TOTP/HOTP is dead simple and, with the open source Google Authenticator app, great for the end user.
e.g. setting up 2-factor with MS with the same email you use for Google will overwrite the Google one unless you rename it.
The Authy app is better.
Look at the screenshots at https://itunes.apple.com/us/app/google-authenticator/id38849... . The buttons are ugly, labels are misaligned, and the colors are ghastly.
Re-ordering tokens in the Google Authenticator app is janky as hell too, and the only way you'll know if it's going to work is if the regular view switches to one with subtly different font sizes.
Authy's not without its rough edges, but it never looks that bad.
From down-thread, regarding Google Authenticator: e.g. setting up 2-factor with MS with the same email you use for Google will overwrite the Google one unless you rename it.
Authy does this correctly.