What's the likelihood of supporting disposable 6-digit codes a la Google Authenticator or Authy? It would be kind of neat to be able to implement this sort of thing without having to request any contact info at all (sites that require phone numbers are annoying, and there's only one email-based option AFAICT); just provide a QR code and tell the user to scan it with their 2FA app of choice, or (optionally) fall back to requesting a destination for verification codes (i.e. for those who don't have smartphones but do have email addresses or SMS-capable dumphones).
I played with SMS, SMS reply, and MMS. All worked well and as expected (I used a Google-Voice account for testing). Probably one of the easiest out-of-band login solutions I've used. For SMS a "link-or-reply" feature would be nice. Depending on the particular use-case it might be easier for me to press a link in the message versus typing something. Also perhaps eventually an app (swiping notification is enough to complete login)
Since this looks like something people can try out and give feedback on, we added "Show HN" to the title for you. This is the local convention. Will take it out if you prefer.