A noise cancellation headphones would help not make you have to pump more sound over the background roar because the background roar should have been tamed down by quite a bit by the noise cancellation. Yes, you’ll have to turn up the volume higher than you normally do at home. But if the headphones has decent noise cancellation (and I find Bose headphones to have the most noise cancellation), then it shouldn’t be too bad.
Another thing I find useful is that even if I’m not listening to anything on the plane (like if I’m sleeping or reading), if I turn off the HA mic volume (but leave them in my ears) and wear the NC headphones on top, it would help cut down the noise by quite a bit.