Is the 2604 really the best opamp to think of. Noise 11nV/root hertz, there are better ones, even a 5532 is less noisy, not that I prefer that one, but how about the AD797 ?
If you care to read the AES paper describing the circuit, you'll see that in the input stage, op-amp noise is dominated by input transistor and feedback resistor noise, especially at higher gains. What you need from the op-amps are enough voltage swing to accommodate the maximum output swing and enough output current to keep the LM394s working at the optimal point on the noise curve. Also, you want closely matched input offset voltages, since the whole thing is direct coupled, all of which strongly suggests a part like the 2604.
There are certainly others to try, however, and there's no reason not to experiment to see if there's something that works better for you. That's one big reason to build it yourself, right?