The reason that Axoloti Core can only output around 2V peak-to-peak is that the +5V voltage from usb (or regulated to 5V from the DC input socket) is considered noisy, and is regulated down to a clean 3.3V for the analog circuitry.
An opamp like the NE5532 can be used to amplify the analog output, but this particular opamp requires a +5V/-5V symmetrical power supply minimum, and recommends a 2V margin between supply and output voltage, so the output swing with a +5V/-5V supply would be 6V peak-to-peak. That would work, but would need to get the +5V/-5V supply from somewhere. Alternatively an asymmetrical +10V supply (or even up to 30V) could work
The AD828 Stereo Preamp Power Amplifier Board Preamplifier Module D has a bit of a confusing name, first I thought it would be a class-D power amp, but it is really a preamp. The AD828 opamp is also a bit of a strange choice as it is designed for video signals. The output signal when using a +5V supply is 3.5V peak-peak, so the optimum maximum gain setting would be around x1.75.
The LMV358 opamp on https://www.sparkfun.com/products/9816 is a "rail-to-rail output" opamp, that means you can get close to 5V peak-peak output swing when powered from +5V. The two stages of x10 gain combined to x100 gain will be too much, it would be better if it was designed for two channels of x2 gain.