I think I get flustered largely because when a customer gets irate, I tend to perceive it as a personal attack. Somehow I'm not measuring up. I'm not doing the job well, I'm responsible for their misery. I think also because Se is my PoLR, I find displays of irate behavior to be rather threatening. I feel like I'm being forced to do something and if I don't comply they are going to get even more angry.
I try to do that too, probably moreso now than I did when I started. When I started in this job, anyone who was angry at me as seen as a threat and not someone I wanted to deal with on any level. Now, at least I've learned to hear them out with a sympathetic ear to the best of my ability, to let them know we are trying to help, to make them feel like they have some options. I have had some successful interactions in doing this. I guess I'm not a complete failure if initially someone is angry at me and then happy in the end (or at least calmed down).
Not all interactions are successful. Some do require the intervention of a manager or even a security guard though.
I couldn't do what you're doing and I greatly envy your skill. The closest thing I have to your situation is handling customers who owe library fines and some get all belligerent when all they owe is a couple of dollars! It's not enough to cause them to lose their checkout privileges. I think it's just the idea that they owe the library money that bothers some customers. I don't think I could handle someone worried about transactions in the thousands, that sounds like a lot of pressure.
I find phone interactions harder than in-person interactions in a way because I can't rely on their body language and oftentimes the voice sounds muffled over the phone. It doesn't help that many of the customers I serve have English as a second language and speak with a strong accent. On the other hand, it is easier to end a transaction over the phone than it is in person if the customer is too belligerent. We do have the right to hang up on overly angry, belligerent customers, especially if they are yelling curse words at us and refuse to stop. On the other hand, it doesn't always seem clear to me enough, at what point do you stop assisting them and insisting they calm down or act more civil before you continue to help them.
I don't typically say 'uhm' but I do say 'yeah' and 'yep.' Maybe I should try using more definitive 'yes.' I never paid close enough attention to that aspect I admit. I have a 3-fix in my enneagram so I do care about how I come across to others and I want to be perceived as successful. It's not my main type and to constantly try to self-promote myself is exhausting.