I set up a test inverting amplifier circuit using the LT1677 opamp:

The input signal was a sine wave from the function generator with peak to peak amplitude of 20 mV and a frequency of 500 Hz and I received an output with an amplitude of about 670 mV and the same 500 Hz frequency, agreeing with the expected gain of -332k/10k = -33.2:

So now I know that the LT1677 works as expected with a negative supply voltage. My issue with Den's original circuit is that I was getting some clipping on the input to pin 2, which didn't seem to be due to any of the capacitors- I switched them all out. I set up a modified version of Den's circuit using a negative voltage input to see if I could fix this clipping issue:

I might reduce the input voltages to +5V and -5V- I couldn't get my inverting amp circuit to work with +12V and -12V. I'll start testing this new circuit next week and start setting up some amplifier boxes.