OK, here goes... ;-)

No, actually you're quite right.
I did say, "you don't need to know the frequency precisely - you just need to know it close enough so that you can get a good enough estimate of the peaks."
The issue is being able to detect the peak value - I think you probably have some good frequency-insensitive suggestions to achieve that goal.

If the amplitude does not vary rapidly, I think the easiest way to get the peak value would simply be to use a rectifier & smoothing cap - the ADC then just measures the smoothed rectifier output...