Keep communicating and keep pushing. Always ask to speak to a superior / upper manager, the squeakiest wheels get the grease!
Your battle with the banks can’t be personal, the person on the other end of the phone is not making judgments specific to you, they are following a criteria. Think about it this way, if it fits they say yes, if it’s a little out of "shape" and it doesn't fit they say no. Their system has little accommodation for any considerations or grey area. You must be persistent and escalate whenever possible to get the outcome you desire.