I think your idea is brilliant but needs a bit o polishing off.
Because every website is different everyone has different requirements, and a solution would be to just use the public key as the identifier instead of the email.
And for backup purposes as master password, I would suggest making it very similar to Trezor and generate for the user with a good RNG a 24-word mnemonic. I know is a hard task to write down for some but you don't do it every day, and you know you're safe if you lose your device or make use of it on a different device. I wouldn't want to rely on the user to memorise it or generate it, especially when users do not generate a good entropy.
I understand is a label, but some bad devs might use it as a way of matching the user, and end users might get confused especially when you can write any email as there is no verification for it in place. Let them choose it, or you make the first one to speed up the process and let them edit it if they don't like "Account 1".
In terms of master password, what do you think is easier to write down as a backup?
This: ?A[ZSOO{PBs&Y]5.6iwm=_t}]t<DOk
Or this: remove maple runway unable empty little swing zebra lava interest secret admit
To create this you can even use the bitcoin libraries, so you don't have to write your own, and you will only need to work on the clients.
If you do it similar to what Trezor did but on a desktop app, you're protocol is built for the web pretty fast. If is good for money is definitely good for Facebook/Twitter/whatever.
If you don't have a lot of experience with bitcoin, you can try to use https://copay.io/ is cross-platform, open source and very secure. Exactly what you're after from my understanding.
You can even change this remove all the bitcoin wallet stuff and make it as an authentication app. It generates the words for you and forces you to back them up to avoid any pain later on. This follows all the principles mentioned.
I've spoken to my bank. No clear answer from them. From my research online there is a service called barclays.net but the fees are high and they provide an outdated software platform with a usb pin-entry system. And none was clear enough to explain if it meets my requirements, on customer support.
Regarding Mongo, i've read somewhere that they don't provide business accounts yet. I've signed up for a personal account and i'm in a queue so far. Also their api has not endpoint for sending payments from what i've seen.
The closest thing i could find to meet my requirements is their private api they use under their mobile banking app, but is heavily secured, and there no chance they will ever give access to that, or allow me to use it.
We just signed with a London based company judopay and they offered us a great deal. They are mostly focused on mobile payments but support rest as well. Our deal is 0.75% + 0.15 with a monthly fee of £100 which i think is really great.
I've had a great experience so far, the staff is very open and responsive.
We originally intended to go with stripe, but they refused us as 'forbidden business' which we aren't as we reviewed their terms plenty of times to see what we fall under. I asked for a clarification/re-review multiple times, but i got no reply which i think is very unprofessional.
Because every website is different everyone has different requirements, and a solution would be to just use the public key as the identifier instead of the email.
And for backup purposes as master password, I would suggest making it very similar to Trezor and generate for the user with a good RNG a 24-word mnemonic. I know is a hard task to write down for some but you don't do it every day, and you know you're safe if you lose your device or make use of it on a different device. I wouldn't want to rely on the user to memorise it or generate it, especially when users do not generate a good entropy.
I would personally recommend using Trezor as guidance. This is my demo: https://cl.ly/1P0N0W1t1a3B
I would be happy to implement it in my systems if it follows the principals above.