I sometimes wear my headphones with no music, just in noise-canceling mode. Just like you, I think music can be distracting or tiring after a while. My Sony headphones have such powerful noise canceling that it silences even the slightest hum, sort of a anechoic chamber. It helps me concentrate and I like keeping my ears warm. If I'm in the mood, I also put some white noise sounds on (youtube has plenty of it) including rain, beach waves and train rides.
And I work in my own private corner office.
> On-ear are the worst (who the F * * * thought pressing your ears into your head was a good idea?)
There also exist on-ear headphones that don't apply so much pressure. So it rather seems to me that the model that you tested simply does not fit your requirements.
I also prefer over-ear over on-ear, but did not have the problem with on-ear headphones that you described.
Besides I really enjoy just silence sometimes, being forced to listen to music does not necessarily improve my focus.