Slow slew-rate of photodiode circuit output
The feedback loop RC network is a low pass filter. To a first approximation, the -3dB point (1/(2*piRC) is currently 72Hz. With the 1uF device, that point was less than 1Hz.

Your plots show the hypothesis to be accurate. I was going to run a simulation, but the TI SPICE model breaks in one of simulators.

You can either reduce the resistor size or reduce the capacitor size or both.

Keep in mind that at higher gain, there is a pole formed at the inverting input by layout parasitics and a small capacitor across the feedback resistor is not merely prudent, but necessary for proper operation of the amplifier.

If you want operation to 10kHz (-3dB bandwidth), then start with a RC product of 1.6E-06.

Note that 220k is a bit high for a feedback resistor; normal practice is to keep this at 100k or less.

As an experiment, try 82k for the feedback resistor and 180pF for the capacitor. You will have lower gain, but the output should not be in slew rate limit (which is what you are currently seeing). These values yield a nominal -3dB point of about 10.7kHz

The maximum frequency to not be in slew rate limit is given by fmax=  Sr/2πVp where Vp is the peak voltage you wish to get from your amplifier and Sr is the slew rate available from the data sheet.