Issue with 2 stage authentication on new Apple iPhone and MacBook Air

I am quite the predicament and my Google searches have not been fruitful at all. I have an iPhone 5 that has now decided to not go past the Apple logo and won't turn on. It appears the battery is swelling and pushing the screen out. I have borrowed an iPhone 6 off a friend and have restored an old backup from the 5 which was fine. I travel a lot and as a result have different SIM cards (many) in various places. At some point I have accepted the 2 stage authentication process with Apple but now have no idea what the phone number is attached to this process and did not make a note of the recovery code (or cannot find it anywhere). I attempted to log in using my Apple ID and have subsequently been locked out. I do not know the phone number to unlock the account. I have phoned Apple support and they advise I need that phone number. My iPhone 5 is the only trusted device I have other than my Macbook but feel even if I gain access it will advise my account is locked and need to know the trusted phone number to unlock. The Find my Phone is switched on so I cannot even do a restore on the phone using iTunes unless this is deactivated and again needs the apple account unlocked. I am at a complete loss and have no way of accessing all the necessary areas to set the new phone up. If anyone has any experience with this or knows a workaround I would be most appreciative.