LED as power generator
LED color -- I agree here; LEDs with lower-energy optical emission should have an effectively wider 'absorption band' in the visible spectrum.

reverse current -- I think this could be problematic. As this is a 'porosity problem' with the underlying diode, I see it presenting a likely loss-path for some/all of your photogenerated current. I would (short of contrary experimental data) look for LEDs with a lower leakage, proportional to forward current.

One item I didn't notice in your list, but think it may prove to be an important factor:
Conversion efficiency -- In my experience with using other components 'backwards,' a component that functions more efficiently when electrically powered (as designed) is nearly always more efficient when electrically generating. Thus, I'd highly recommend using LEDs with proportionally higher light output/electrical power efficiency ('color temperature' may not apply here, due to the LED color argument).