The simplest way to overcome this is to switch to a FET input op-amp, such as the TL072, which will have tiny bias currents, around the same order as the leakage current through a capacitor.
Have you considered a FET input op-amp? They really aren't that bad and with the input impedances you have, the noise will be similar to a bipolar op-amp in the same price range.
I forgot to mention the difference in noise between BJT and FET input op-amps such as the NE5532 and TL072 respectively.
With a low input impedance, the NE5532 will have lower noise than the TL072, since it has a lower noise voltage. At higher input impedances, the TL072 will be the least noisy, since it has tiny bias currents and the large bias currents of the NE5532 and their associated noise, will generate a corresponding noise voltage in whatever impedance is at the inputs. From memory the crossover point when the TL072 becomes better than the NE5532 is around 30k of input impedance, which is not far off what this circuit has.
Unfortunately I didn't see a specification for the input noise current on the NJM4580, which doesn't inspire confidence with that characteristic. I doubt it's better than the NE5532 and even if it is, then TL072 will still be better because the lower bias current through the pot. is worth it.
The input impedance of my guitar amplifier is rated at 1Meg ohms. I'm assuming
that they were expecting the source impedance (guitar) to be at max 100K ohms.
Does the circuit that I posted have around 19K ohms input impedance? (R5 ||
R1). That really makes using a FET input op amp more correct in this case. I
stuck with using the NE5332 since that was what's on the original schematic,
but it looks like I'll have to use a FET input op amp to easily avoid the
offset currents that I don't want.
Another (unrelated?) question that I have, how do I calculate the current
consumption of an op amp circuit, for power supply sizing? Would it simply be:
((expected max Vo of the op amp) /
(max impedance of the feedback network)) +
quiescent current of the op amp?