How to estimate the mean of a clipped signal?
Is this crazy? Good? Done before and has a name?


I wouldn't say that it is "Good" because clipping is not noise that can be modeled as an additive component with some distribution.


  fit a curve over the top 3 or 5 highest bins, and the position of the
  peak is the signal median


The position of that peak would be the modal mean, not the median

The effect of clipping on the signal's distribution would be to a) truncate the real distribution (whatever that is) at the maximum (which depends on the sensor &amp; measurement (or "environment" as you put it) and b) distort the distribution towards this maximum depending on how much clipping was present in the signal.

b) means that whatever you do, your median / mean will be biased by the amount of clipping.

Ideally, you would have to change the sensor to one that can respond to higher accelerations.

If you absolutely must use the current sensor and deal with the clipping then prior to any further processing of its output you could try removing the clipped values (with a simple thresholding operation) and fitting a curve to the data. If you were to fit an spline for example, then the curve would depart at the beginning of the clipped part with the slope of the usable signal prior the clipping and arrive at the end of the clipped part with a slope of the usable signal after the clipping. In this way, all clipped parts will be converted to some "soft" peak (because of the splines "smoothing" effect). 

Of course, this is a compromise. It could well be that the clipping is so much that very little "usable" signal remains on either side to fit a "good" spline. Furthermore, depending on your sampling frequency ($Fs$), the signal might be full of impulse-like data which would lead to "very tall" splines as the algorithm would try to fit the sharp slopes. More information would be needed to take a decision on that but in general a higher $Fs$ would help.