Eqev: Who Inscribed the 2nd Luchos?

Given:
Hashem both carved and inscribed the First
Luchos

And Moshe hewed the Second set of Luchos

Who inscribed this second set?

We have some ambiguities in the text.
And we can resolve them by means of the 13th principle of Rabbi Yishma'el namely:

'Vechein sh'nei ch'suvim hamach'chishim ze es zeh..'

First the conflicting
Shnei Ch'suvim:

1 Shmos 34:1 HKBH is Writing 2nd luchos
"V'chasavti al halluchos"

2. Sh'mos 34 "K'sav lecha.." Moshe is writing on {luchos? Or something else?}

Not a complete contradiction, but an ambiguous one

This week's Parshas Eqev to the rescue!

The scale tipper -
Hakkasuv hashlishi:

3. Dvarim Eqev Ch. 10:2-4 "v'echtov al halluchos" where it is clear that HKBH wrote on the 2nd Luchos.

I think this structure is clear. And therefore in #2 Moshe probably wrote something else or wrote the dibros UPON something else E.G. parchment.

KT
RRW