Thanks, @rgo!
It’s nice to not be the only one staying up at night thinking about this parametrization 
That under and overshoot has kind of been my motivation to explore this topic as well!
Loved the graph tool! 
Very easy to manipulate that curve without accidentally breaking it!
I did kind of the same thing in Python using streamlit: https://share.streamlit.io/jandren/tone-curve-explorer
It would be a pleasure to merge your proposal in there if you want to come with a PR! Not sure how to support the nice in graph interaction though. Anyway, you can find the code here: GitHub - jandren/tone-curve-explorer: A simple streamlit app to explore the shapes of some tone curves.
Fun note, the Michaelis-Menten curve is often called Reinhard tone mapping in image editing if x is your scene-referred pixels.
There is a lot of content over at the sigmoid thread, don’t know if you read it or if it will help in any way but here is the link regardless: New Sigmoid Scene to Display mapping