ok, but I'm not sure how you're getting entropy in there, since your examples are only to calculate enthalpy at one temperature from enthalpy from another.

There are relationships between entropy and heat capacity, so you maybe could make some substitutions, but they generally make some assumptions about the way the system is changed (constant volume, constant temperature, reversibility, etc.) that may not apply here. I'd have to work it out on paper to see how that version of Kirchhoff's equation is derived, then maybe you could understand why it isn't giving you the correct answer.