Oh, I know what you mean. In my experience, constant low hums like that can be weirdly soothing until they're not. My niece used to sleep through street noise but a dripping faucet would wake her up every time.
Did a fan ever help you with that kind of noise? I found that a constant fan sound covers up all the little bumps and drips so I can sleep. It made a big difference for me when I lived in a noisy apartment.