David,
Feedback is caused by gain, the microphone hearing the speaker and reproducing it, not “because an amp loses it's flat response as you push it harder”.
If you put a hard limiter on your monitors, you can cause them to feed back with under a watt, at a very low SPL, which can be useful for finding rings without blowing ears or drivers.
In the same fashion, if you don’t have enough power for your monitors to get loud enough, you may turn them up to increase the average level causing feedback, and the peaks will be clipped, a basic (nasty) form of limiting. The clipping will be heard more in the HF, where the clipped harmonics are more prevalent and your ears are more sensitive to distortion, the “exaggerated frequencies” you mentioned.
With more power, the peaks are reproduced without clipping, so the monitor gets louder, the performers don’t have to sing (scream) as hard, until enough power is put in and thermal compression sets in...
Art Welter