LGG formulas can’t work with scene referred linear data.
Also note that the Sat formula uses REC.709 constants, and should instead be customizable, or auto-filled software depending. The clamp featured in the ASC is also a problem for some implementations, including ACES, which has it removed.
Fulcrum based Power is also easily achieved via a simple divide by fulcrum → Power → multiply by fulcrum chain.
Manipulations should all be applied on linear, ideally scene linear data, hence why most contemporary pipelines have an assumed fixed reference space with a scene referred linear model, and tack on the nonlinear camera rendering transforms as a non-destructive view. Calculations / manipulations are all done against the scene referred linear values, and transformed under the camera rendering transform, keeping the reference space always linearized.