Splitting a bidirectional bus into two unidirectional ones
I abandoned the original circuit and got it working with a different one. The keyword to look for here is I2C isolation. Because isolation is by definition unidirectional, bidirectional channels like I2C have to be separated before they can be isolated. Texas Instruments has a nice document describing two different methods for isolation.

One of them (ISO154x Method) requires different voltage levels on both sides of the isolator, so that was not feasable for me. So I went for the other (ISOW7842) method. There is a separate document that explains this circuit in detail. I also found an Electronic Design article on the same topic using the same circuit. It includes a detailed calculation of the fine tuned resistor values.



By simply omitting the isolator and grabbing the signals from the separated lines, I was able to achieve what I want. For me only one of the directions was actually separated, but by substracting the signals, one can get both directions indivudually quite easily.