Not sure what your budget is, but take a look at Sony MDR-Z1R. I wear them to bed sometimes. They're kind of big, but are pretty light and very comfortable. Lots of detail, fairly neutral, maybe a little bass heavy.
My favorite bedtime headphones are Sennheiser HD 6XX, super comfortable, but you already have Senns and these are also open back and probably sound similar to your Momentum.
I don't have any experience with the Chord. I'm using Sony's TA-ZH1ES headphone amp.