Jeff, when you say "more precise" are you meaning a more narrow band/Q? That I'd have to research but I'm not sure that's a good idea to mess with that. If you need surgical narrow-band boost-cut then I'd use an external eq. Otherwise I think wider band boost/cut eq is generally more musical or at least tame. This is assuming you're like me and you don't like using eq and if you do its in small amounts.
As far as noise and making it "better", recapping the eq section is likely not going to hurt and using good quality low ESR caps is a good start though I don't have any qualms with the parts Tascam spec'ed in there...they aren't on the "crap" list of caps and every cap I've tested that I pulled from 80's vintage Tascam gear was still in spec as far as the capacitance...never tested the ESR though which is THE definitive test for caps. I don't have an ESR meter.
Outside of recapping, putting different opamps in the the eq section may help with noise and clarity...a faster amp could minimize phase distortion and such that results from slew rate issues (i.e. how fast the amp can respond to dynamic changes in the input to the output) though the stock TL072's aren't a bad amp...they get a bad rap because they're everywhere but they're everywhere because they're not bad, and they're cheap...because they're everywhere.

Its important to understand that the quality and/or performance of an opamp-based audio circuit has as much to do with the surrounding circuitry as it does with the choice of opamp and that goes both ways; a different opamp may make noticeable improvements -OR- a path with an "older" opamp may sound really great in spite of the almighty spec-sheet
because the entire circuit was a good design. But the 072
is "garden variety" and there's no harm in trying something else out you know? I'm conservative and probably the safest best bang-for-the-buck amp to try would be the OPA2134. It may not be necessary to bypass the power inputs to each of those amps if you put in the 2134's (i.e. putting a 0.01uF film cap across pins 4 and 8 of each opamp...it will prevent the chip from oscillating though some say there's not as much a concern over the 2134 being a problem in this way) but its good practice anyway. The eq section opamps are U5 and U6. One half of U5 is the input stage and the other half is the LF band amp...U6 is for the MF band and HF band. U7 is also involved...one half of U7 is the output stage from the eq section but U7 is a 4556. The other half is the output booster amp for the channel. You could stick a 2134 there too but the only hitch is that Tascam put the 4556 there because it has a
rediculous amount output current potential (70mA) and they did this because that one amp section drives audio to all 8 PGM groups as well as the SOLO buss. There is likely an engineering buffer there and 70mA of drive is probably never needed even if you are running all of those busses wide open, but how much is needed? Dunno. At the time the M-500 boards were being made there was a wide gap in output on offerings as far as good audio opamps. So you had parts that had drive in the teens of mA and even into the lower 20's, and then you had the 4556 at 70mA. The 2134 is rated for 35mA of output current which is good. Maybe it would have been good enough back in the day. Probably good enough for U7 assuming you don't simultaneously buss to all 8 groups.
So you could start with U5 and U6 and see what you hear and if you aren't satisfied you aren't likely to get any benefit to the eq section by replacing U7 because it is on the output side (of the eq section and the channel strip).
The other thing you could mess with if you are recapping is to increase the capacitance of the coupling caps in the eq section. Look at C12 and C25. C25 is the input coupling cap. The bigger the capacitance, the better the LF performance at a sacrifice to HF performance so there is a balancing act BUT HF performance of electrolytic caps has improved over the years (related to better and better ESR specs) so the balancing act is easier to manage. In cases where the capacitance is large you can bypass the large value electrolytic with a small value film cap (i.e. put the film cap in parallel with the electrolytic). By small value we are again talking about 0.01uF. With the two caps in parallel you are getting the LF benefit of the larger electrolytic and the HF benefit of the small value film. Some people go bonkers (IMO) and bypass everything with the film caps. I'm conservative. I feel at values that we are dealing with with these coupling caps it is overkill. I feel it is satisfactory to just use good quality contemporary low ESR caps, and to spec 105C temp rated parts. This is why I like the Nichicon KT series;
105C rated "audio grade" caps...dunno what that all means but the ESR spec is good, they're relatively cheap and I've been happy with them. Okay...so...back to the original point. The input coupling cap C25 is 10uF. Remember that the bigger the capacitance the lower the frequency the cap will pass. A 10uF cap has a -3dB point of about 26Hz. That is pretty high IMO. There are a couple reasons why this may have been done and one is to build in a high-pass filter so the operator doesn't inadvertantly overload the channel with high energy LF signal...the other may have been to control what the opamps had to deal with in terms of spectral content. OR it may have had some to do with that balancing act and wanting to make sure that HF performance was less limited going into the eq section. Sometimes you also see ALL coupling caps having the same value because the manufacturer got a better deal going with one value across the board thus being able to get them in large quantities and get better pricing. I actually see a lot less of this practice in Tascam's designs than a lot of other makes, so I think the selection of the 10uF cap at C25 to have been the result of a purposeful design element. At any rate you might consider increasing that to 47uF or even 68uF, and same goes with C12 which is the output coupling cap from the eq section. 47uF gives you a -3dB point of about 6Hz and 68uF sets it at about 4Hz. That gets the coupling caps out of the way of effecting the spectral content of what goes into and what comes out of the eq section. I'd be more apt to monkey with the coupling cap values if I was putting a different opamp in there for U5 and U6 just because something like the 2134 is going to be more capable of dealing with what's coming in than the 072, not that the 072
can't deal with a wider spectrum. A more conservative approach might be to just roughly double what's there...change C25 to 22uF and C12 to 47uF and keep the stock 072's. See what you think and tweak from there.
The last idea I have with regard to the caps is to put non-polar caps in there rather than polar caps. They might have done this from the factory but non-polar caps are much more expensive and the benefits of using them for coupling may be more paper-based than ear-based if you know what I mean. But you can use non-polar parts here since the power supply rails are bipolar. I'd use Nichicon EP (105C) or ES (85C but "audio-grade" MUSE series parts) if you wanted to try non-polar. Might not hear any difference but putting something like the ES caps in there, upping the capacitance and swapping out the 072's for 2134's would be MY personal nth degree treatment. Again, I'm conservative and I wouldn't go further than that.
All the small value film caps in the eq section determine the frequency ranges. If that is something you want to mess with you're going to have to wait for somebody with a lot more knowledge than me.

I don't know how to make those calculations. Many do though.
The final point you have to realize to all of this is that if you focus on the eq section only its like plumbing...You replace one section of old galvanized pipe with pex because you've got low flow from the galvanized being all corroded and built up with scale inside. That one section of pipe will perform better, but you've STILL got the supply to the house and everything in between. Your water is still going to taste like rust and you're not going to improve the flow until you go back to the source. Don't take it that I'm saying the stock M-520 channels "taste like rust". Get my analogy here; you've still got C1, C2, C10, C11, C46, C47...