It always seemed Pashut to me that Moshe carved the second set of luchot and that Hashem wrote on them.
Once, a Rav happened to briefly mention that Moshe wrote the latter set of luchot in his drasha. I found this far-fetched at the time. Today, I find it completely untenable.
Just take a look at the parsha. It seems clear that Hashem wrote on the second set of luchot. (Eqev: 10: 2-4)