Remember, just because a newer, more expensive op amp can be installed where a garden-variety NE5532 or TL082 used to be doesn't automatically mean that it'll work better (or work at all) and there's certainly no guarantee it'll sound better. The ridiculously acclaimed Benchmark DAC-1 is an example of a device that achieves phenomenal performance out of garden-variety op amps through superb design implementation rather than throwing expensive parts into a box. There may very well be places in your console where a better op amp won't have any audible effect at all, and then there will be places where a newer, faster amp can cause stability problems. The trick here is to do your homework, which means downloading and comparing data sheets, reading books like Walt Jung's op amp treatises and of course asking questions here. You've already gotten responses from some very knowledgeable people. Their opinions will vary wildly, but they know how to achieve the results they're after.
You need to move slowly and confirm your upgrades really are upgrades before you repeat them across multiple channels. The first step before you begin any chip replacements is to make sure the console is in good stock operating condition. Give the power supply a tune-up or an overhaul as necessary, make sure all the logic functions are working, get your switches cleaned up and so forth before you start messing with chips. There's no point in spending a couple grand on ICs to reduce your distortion from 0.01% to 0.003% if your switches are noisy and you have leaky, dried-out caps all over the place, squirting DC current where it isn't wanted and degrading performance by a greater margin. Get your hands on an oscilloscope and see what's going on at various places around the console in the non-audio range. An op amp can't do a great job of buffering an audio signal if it's busy pumping out full-scale oscillation at 250kHz or 3MHz.
Once you're ready to start working, work in the following order. First take care of the power supply and any motherboard regulation or filtering. Then move on to the modules. Do the MONITOR SECTION FIRST. The module that routes signal to your speakers. It does no good to improve the channels and busses if you can't hear the improvements. Besides that, the monitor section is relatively small and a good place to get started. Replace one thing at a time, and listen/measure for changes before you move on to the next part. If a chip upgrade causes RF oscillation, you'll want to know about that before you mess with anything else. It's much easier to find when you know you've only changed one part. As you start replacing opamps with more precise chips you may decide to short out some coupling caps, but that can be trickier than it sounds. There's more to getting rid of DC offset than just buying precision amplifiers. If you do decide to DC-couple some stages, you need to measure the DC voltage on both ends before and after the upgrade and the cap elimination. Learn what all the input offset, input bias current, and drift terms mean in the data sheets and how to predict what a chip will do in a given circuit. It's really not that hard, just some basic algebra.
After you've finished the monitor section, then tackle the master section. Do the main stereo buss first, then the subgroups. Do them two at a time, so you have a stock stereo pair with which to compare an upgraded pair. If you move backward through the signal path like this, you'll always be able to kill all "non-upgraded" inputs to a section and see if it behaves by itself. After the master section is done, and you're already burned out and broke from chip upgrades, then you start thinking about the channel modules. Again, tackle two at a time and take it slow. Spread the work out over a period of time. Most people can use their console and get work done with a couple of channel modules missing, so set a goal of maybe finishing one pair of modules each week (or day or month or whatever your workload permits) until you finish. When you finish this slow methodical approach, you should have a very good idea of which upgrades produced the most significant sonic improvements and which were a waste of time. Then you can share your knowledge here with the next poor guy who decides to spend his student loan on a big Digikey order. Such is the circle of life.