What if you were to replace either the 10k or the 1M with an LDR so that the 'eye' has some ability to adjust its sensitivity to different ambient light levels?
I don't think that would work. It would not adjust the sensitivity of the sensor, simply change the output. You might tend to think that is the same thing but it isn't.
The IR sensor can become saturated, that is no amount of extra light will produce any extra signal, that is the limiting factor with interfering light. The amplification applied to the sensor's output simply sets the voltage you get when this saturation occurs it will not affect the point at which the sensor becomes saturated.