I don't think anyone ever seriously questioned that writing had not been invented by the time of Moses. Writing clearly existed even before the usual dating of Noah.
Yet that was the basis for the Jahwist conclusions
Not really. What Jesus did was refer to the Torah as "Moses", a very common usage in 1st-century Judaism. He did not actually say that the historical person Moses wrote the Torah.
The attribution of the Torah to Moses was made by the post-exilic rabbis. And this was where the practice of calling the Torah the Law (or teaching) of Moses,--or simply, "Moses"--came from.
No Christ is not deceitful, nor did he speak a single wrong word, He is God and as such is absolutely beyond reproach in what he says. Christ was accurate and he did not refer to the Pentateuch as Moses, He said Moses wrote of Him.
You are being true to the scripture though for you do not believe Moses and as such do not believe Christ when he says that Moses wrote of Him.
Matthew 22:24 "Moses said, 'If a man dies without children...'"
Mark 7:10 "For instance, Moses gave you this law from God..."
Mark 12:24 "...haven't you ever read about this in the writings of Moses, in the story of the burning bush..."
Luke 24:44 "...I told you that everything written about me by Moses and the prophets and in the Psalms must all come true."
John 1:17 "For the law was given through Moses..."
John 5:46 "But if you had believed Moses, you would have believed me because he wrote about me. And since you don't believe what he wrote, how will you believe what I say?"
John 7:23 "...do it, so as not to break the law of Moses..."
Passages elsewhere in the Christian Scriptures:
Acts 26:22 "...I teach nothing except what the prophets and Moses said would happen..."
Romans 10:5 "For Moses wrote..."
New International Version (©1984)
If you believed Moses, you would believe me, for he wrote about me.
New Living Translation (©2007)
If you really believed Moses, you would believe me, because he wrote about me.
English Standard Version (©2001)
For if you believed Moses, you would believe me; for he wrote of me.
New American Standard Bible (©1995)
"For if you believed Moses, you would believe Me, for he wrote about Me.
King James Bible (Cambridge Ed.)
For had ye believed Moses, ye would have believed me: for he wrote of me.
International Standard Version (©2008)
because if you believed Moses, you would believe me, since he wrote about me.
Aramaic Bible in Plain English (©2010)
For if you had trusted Moses, you would also trust me, for he wrote about Me.
GOD'S WORD® Translation (©1995)
If you really believed Moses, you would believe me. Moses wrote about me.
King James 2000 Bible (©2003)
For had you believed Moses, you would have believed me: for he wrote of me.
American King James Version
For had you believed Moses, you would have believed me; for he wrote of me.
American Standard Version
For if ye believed Moses, ye would believe me; for he wrote of me.
Bible in Basic English
If you had belief in Moses you would have belief in me; for his writings are about me.
Douay-Rheims Bible
For if you did believe Moses, you would perhaps believe me also; for he wrote of me.
Darby Bible Translation
for if ye had believed Moses, ye would have believed me, for he wrote of me.
English Revised Version
For if ye believed Moses, ye would believe me; for he wrote of me.
Webster's Bible Translation
For had ye believed Moses, ye would have believed me: for he wrote concerning me.
Weymouth New Testament
For if you believe Moses, you would believe me; for he wrote about me.
World English Bible
For if you believed Moses, you would believe me; for he wrote about me.
Young's Literal Translation
for if ye were believing Moses, ye would have been believing me, for he wrote concerning me;