If you could share the image you have used to show the slippage I would try to remap the histograms as I did for my own picture.

EDIT. In fact that’s simple. I’m able to reproduce the same histogram with any value of grey just in changing the black point. I haven’t the non well balance image you talk about but I don’t see why the behaviour would be different.

Some maths to demonstrate it.

out = (log2(input / grey) - black) / dynamic_range

let’s say I change grey to grey1.

out1 = (log2(input / grey1) - black) / dynamic_range

If I try to get back the initial out with this grey1 just playing with black point:

out = (log2(input / grey1) - black1) / dynamic_range = (log2(input / grey) - black) / dynamic_range

(log2(input / grey1) - black1) = (log2(input / grey) - black)

log2(input) - log2(grey1) - black1 = log2(input) - log2(grey) - black

black1 = black + log(grey) - log2(grey1) = black + log2(grey/grey1)

This is valid for all inputs (well balanced or not, clipping aside)

I understand that grey value is introduced in the equation merely to transform the input into stops but doesn’t transform the shape of the log.

I’m afraid I cannot do better to convince you that 2 inputs are enough to define a portion of log curve (as for a portion of line) and the grey slider is useless.