The two left most yellow cap should be for bypassing of the voltage supply rails for the op-amp.
So you should need 12V cap at minimum.
You said that you have replace them with 1000uF caps, and from the photo you are using 8mm dia OS-cons.
I don't 1000uF OS-Con for 16V or higher exist, so something must be wrong here.
I'm not sure how 0404 regulate it's +-12V supply for op-amp, I will take it as there is a 4.7 ohm resistor before the yellow 10uF caps to filter noise. In that case 10uf should be quite fine. (PPA schematic used only film caps after the resistor)
Personally I think 10uF is fine, and more than 100uf is pointless, but there's nothing with using 1000uF either.
I don't see that there will be any major problem with changeing it to 1000uF.
But there's one potential danger in doing so. that is if I'm right that the caps are for bypassing +-12V supply for op-amp, there's 4.7 ohm resistors before them, and that there's no muting circuit when you turn on the power (as I have seen in 0202 with the huge 1000uF cap).
for 1000uF cap takes 100 times longer to be charged to a certain voltage compared to 10uF caps. And because the existence of the 4R7 resistors before it, the current supply to it is limited.
So for that few ms that the caps are charging up, the output op-amp will be getting voltage supply that's below its rating. And when this happen the op-amp will not be stable. (this is the main reason that you hear a pop when you turn on some instruments) The worst case will be it outputing huge DC offset (that could be up to rail voltage, who knows?)
In the worst case you connect the 0404 to a headphone amp with gain 11, and then to a earphone of Z=16ohm.
If you take the DC offset as 1V, the amp make it 11V, and since power=V^2/R, your tiny 16ohm imp earphone will be heated at a power of 7.56Watt, i.e. 7.56mJ per ms, which will burn burn it in just a few ms even if the diaphragm don't break with the loud pop.
For 1000uF to be charge to 12V with a 4R7 resistor, it takes 9.4ms (if my maths serve me right), and in that period of time each of the 4R7 resistor will converted 0.144J to heat (the initial peak power is 30.6W!!!), which I'm not sure is safe.
Luckily most op-amps are operational from +-5V onward. the popular AD8620 works well down to +-3V (personal experiance), and for it to output DC it may takes much lower voltages.
For 5V the time will be 2.5ms, for 3V it will be 1.33ms.
So in practice it's quite safe as long as you don't have a killer combi of a low Z phone with a high gain amp that's on when you switch on your computer.
well, things will be much easier if you just use 100uF or less...
Also can let me know where you get all your OS-CON from?