That sounds to me like you're trying to cheat physics here. If there's a physical limit to calculating an irreversible G(X), I don't see how you magically remove it by pretending that something including G(X) is reversible and then by ignoring what you've just added.

What I'm trying to address is the claim that there is something 'interesting' about irreversible functions that you can't do using reversible functions. Irreversible functions just discard information in the course of calculating some value. You can simply save the discarded information and have the same calculated value in your result, and have a reversible function. Nothing about this violates physics. Obviously it's not exactly the same function - it has more outputs and inputs. But it can be used as a subcomponent of any operation where you needed the reversible function. there is no such thing as a class of 'interesting' functions which cannot be used in this way.

What is the size of the "nondiscarded information" you must save in this case?