I’m a light sleeper. That sort of noise throughout the night would prevent me from sleeping as well. I’m pretty well able to flex but even 1 night without any sleep would be more than I could handle.
I’ve not experienced anything like the OP. But if I had, the key to success is being persistent and polite. I would have been mollified with a change of cabin and FCC. I’m claustrophobic too, but don’t have a problem with inside cabins. The $250 sounds light to me. I would have politely asked for more. If the rep had told me that’s all that he/she could do, I would ask to speak with someone who has higher authority.