I reconfigured the three channels so they were in series, whereas before they operated in parallel and fed into a mixer. Here's the schematic:
The series configuration is an improvement because, when parallel, the weight given to each channel in the mixer is dependent on its gain. This allowed for the unintended behavior of two channels set near unity gain overpowering a third channel that may be boosting or attenuating a frequency band. Arranging the filters in series takes the product of their gains rather than summing their effects. This is the correct behavior.
I tried to increase the range over which the gain of each channel could swing by setting R3, R5, R6, R8, R11, & R13 to 1KΩ as opposed to 10kΩ, their original value. The capacitors in parallel to the potentiometers limited the maximum impedance of the potentiometer, capacitor network, and thus set an upper limit on the range over which the gain could move. Still, making the change from 10kΩ to 1kΩ had such a strong effect on performance that adjusting the bass channel to about 2/3 of its maximum gain caused noise to grow out of control. This needs to be fixed.
The new circuit is working a lot better, but I still need to make a ton of refinements. Up through now I've been designing according to the great principle of TLAR. Now time to dig in and make this guy work a lot better. Additionally, I need to add a boost converter of capacitively couple the output so that I can power the circuit from a USB port. Getting USB power complicates things because the ground line in the headphone jack needs to be the same as that of the USB port. Otherwise, if the ground line going to the headphone jack gets connected to earth ground via whatever speakers you plug in & the USB port is also connected to earth ground, you could short these two potentials, causing significant damage to the equalizer, the speaker, or the USB port.