Those controls in Lightroom are great, but looking at the research papers linked above, Lightroom doesn't give the user complete control over the process. There are a lot more than three parameters that could be changed. If the user had complete control over the contrast curve that's used to control the algorithm, it would be possible to control the level of bright details separately from dark details, for example, or to decrease fine details while increasing larger-scale contrast, or any number of other subtle variations that aren't possible in Lightroom.
Because of this, I'm wondering if there is software that offers a similar edge-aware processing technique, but with a more advanced level of control.
The only ones I'm aware of are Adobe Camera Raw (which offers the exact same controls as Lightroom) and Silver Efex Pro 2, which I think uses a different algorithm but with an effect somewhat similar to the clarity control. (It does offer a distintion between "structure" and "fine structure", but the level of control is still very limited.) It seems there is also a programming language called Halide that also offers this algorithm, but I was hoping to find it in the form of a photo editing application.