Thanks for the advice. Agree Twitter is the best customer service channel.
As it goes I did contact CS but they told me they couldn't help and there was no way to re-access or de-activate the account without me having a way in.
I luckily just managed to fix the issue by logging in with my Google account (had also enabled this) which allowed me to change phone number etc. without needing to use 2-step authentication - which is odd, but good.
But other than that, there would have not been any way to access the account.
Other apps, where I've mistakenly had this same issue (for the same reason: change phone, change device) have been able to temporarily disable 2-step verification for me once I prove my ID. But not Evernote, who tell me they have no way to ever access the account ever again.