When I go to https://my.nexcess.net/ in the most recent version of macOS and Safari, I'm prompted for my fingerprint to autofill the Email and Password fields. So far so good. then select all of the mountains, or sidewalks, or boats, or motorcycles or whatever Recaptcha is making me do and click 'Login'. (That is if I pass Recaptcha, which is often harder than it looks.... is that a "mountain" or just a little hill or incline?)
I'm now taken to another login form, this one has the Email and Password fields again, but filled in. It also has an 'Authentication Code' field, a 'Remember this device for 30 days' field, and another Recaptcha to try to fill out. If I click in the 'Authentication Code' field it should offer to autopopulate my authentication token, but it does not. Instead it will fill in my password at which time it will say 'Invalid Authentication Code'. (I suspect it does this because the input type is "password", which isn't a common way of handling 2FA token fields as they are not sensitive information in the same way as a password.)
At one point there was another bug here that actually prevented me from typing in the authentication code unless I edited the HTML source of the page to change the input type from password to text. It looks like that is now fixed.
So at this point I go into the System Preferences to grab the authentication token, paste it in, click the 'Remember this device for 30 days' checkbox which never remembers me, and go through the Recaptcha again. Now since I've had to go through the Recaptcha, the token I've typed in has likely expired.
Your fiends over at Liquid Web have this working really well. Perhaps you could get some input from them. Their Dashboard login form doesn't prompt for Recaptcha, and auto fills in the username, password, and authentication code with Safari/macOS seamlessly.
Additionally, the user I mentioned on Twitter, @rmondello, is an engineer at Apple working on their Keychain (password mamanger) product, 2FA implementations, etc and they have indicated a willingness to help here too.