Why is a mixer full of TL071's sad? Does it actually sound bad? If the frequency response leaves a little to be desired perhaps all it needs is a thorough recapping.
Many older Tridents and other wonderful desks were full of TL07x IC's, and most of the 'upgrades' I heard for those boards (using 'superior' components) don't sound as nice as a well-maintained stock unit.
What brand/model is your mixer? Do you actually dislike the performance, or do you simply believe that more recent IC's would yield better performance? You might be surprised.
Just a thought.
If you absolutely insist on replacing the 741's then try Burr Brown's (now TI's) OPA604. It's a pin-compatible FET op amp, but watch your current draw. Make sure the power supply is sufficient.
I suggest you upgrade only one channel first and then compare to see if it is, indeed, an improvement.
JC