As far as designing circuitry, my kit building days never took me that far.
I'll either copy something that already exists, or buy something.
So if neither exists already, then that will be my queue to modify my plan.
Blender preamps are common, but I don't know about the three-mic input requirement. That would at least require some consideration of blending the three mics before the commercial blender pre, and you might need to consider filter circuits as part of that circuit.
One thing I do know quite well is the physics of sound. That's why I know that if I put a mic on the upper and lower edge of the fretboard, that i'll get a very good balance of the two.
And I know that IF I could overcome the physics of the sound hole, that putting a mic in the middle would give a very good fill to the outside pickups.
See, I think your problems are acoustic, not electric. The physics of sound say that multiple mics can create phase cancellations. That is ameliorated somewhat with surface-mounted mics, but at the distance you are talking from the strings I wouldn't count on that.
The physics of sound also say that every time you double the number of open mics gain before feedback drops 3dB. Sound engineers generally strive to have as few open mics as possible on a stage. Having multiple mics on a guitar doesn't help; you can compensate by turning all of them down, but the nature of the multiple mic system could mean the system has resonant frequencies that will be more complicated to ring out than a single mic.
The physics of the soundhole are quite simple: it's bassy. You can compensate for that with a filter circuit, but the required correction will be greater with a cardioid mic than an omni. I don't think all of your troubles go away with the omni; the filter circuit is still required, but it's probably 6dB/octave rather than 12dB/octave. And still you have the problem that you aren't capturing the natural sound of the guitar. Sure, you could stick a tiny omni underneath every string and blend them, but that's more akin to an electric guitar sound than an acoustic. If that's what you want use a magnetic pickup.
But let me point out that I have seen multiple mic solutions on acoustic with mics inside the body. Condensers, dynamics, piezos on sticky pads, in beams, you name it. There's no mic method that can't yield good results if implemented correctly. Again, this is where I need advice.
But I can't give you advice unless I build the system and determine how to compensate for its idiosyncrasies electronically. This is not an electronic problem, it's an acoustic problem that requires an electronic solution. Eliminate the acoustic problem and the circuit becomes very very simple.
So sure, anything can be implemented, but does it actually sound better than a different solution? That's why I suggested a control technique for comparison.
Now, back to your comments. I have no problem switching over to omni mics to get this done.
In fact, I had actually thought this through, and was planning on using omni mics at the edges of the fretboard in order to take advantage of the boundary effect.
The boundary effect is not a function of polar pattern, it's an acoustic phenomenon at a surface. There are cardioid boundary mics although most are omni. Given the boundary principle, an omni is perhaps a more obvious choice although anything works.
My only reasoning for the cardiod in the soundhole, is to avoid an imbalance between the amount of signal that mic takes in, vs the two on the edge.
Has more to do with distance from source than rejection. If the mic is flush with the soundhole, the difference in distances from middle strings to side strings would have a larger effect than the cancellation at 30 degrees off-axis, which is practically none. Of course those differences in distance are also potential sources of phase cancellation, but we've discussed that.
Look, your system is quite easy to audition without drilling: buy the three mics you want to use and patch them into a regular ol' mixer. Aim them at your guitar at the same distance they would be installed. We have already learned that the cardioid pattern doesn't matter in terms of the soundhole, so it should sound roughly the same whether aimed at or out from the guitar.
Record that and blend to taste. Note any EQ corrections you have to make and decide how to handle that when you build the preamp.
Compare with two other techniques: one of the mics attached to the lower bout, and a pair of the mics aimed at the 12th fret and lower bout from 18" away. If you can get your system to sound better than (or at least as good as) either of those approaches using a reasonable circuit, then install it in the guitar.
One last thing to consider with these little capsules is that attention must be paid to circuit design to prevent overloading their FET. An
acoustic guitar string at 1/2" could be rather loud. This varies a lot by the capsule in question, so again it's hard to make specific recommendations.