Several points in your last popint still point to the SRH-940: (1) 440 lacking in bass - the 940 has zero bass emphasis, but it's actually very close to the Senn HD800 bass, so a good choice. (2) Like to hear what's in the recording - 940. (3) Air and space at the top end - 940. (4) Other headphones treble rolloff - not the 940. (5) Home listening, large size - 940.
To get better sound and detail than the 940 at any price, what would be the next step up? I've had about 100 headphones in the past 3 years, so I'm looking at my list for the next better headphone than the 940: Nothing until the Sennheiser HD800, unless you're looking for a different type of sound, such as warmer bass.