Rosh HaShana, Yom Kippur, and Shabbat

In Vayikra 23 and in Bamidbar 29, the laws of Rosh HaShana and Yom Kippur are given. They only appear in P (and/or R), not in D, J, or E. Moreover, Rosh Chodesh is only given in P, in Shemot 12, with a remembrance appearing in Bamidbar 10:10, also a text of P. But Rosh Chodesh does appear, together with Shabbat, in the prophets before P (e.g., Hoshea 2:13, Yeshayahu 1:13).

Therefore it seems that the law in E did have Rosh Chodesh, but it had to be deleted because, in the same context, Shabbat was mentioned as the day of full moon (see the work of Meek, or its modern-day version), day 15 of the month. That day was cancelled, according to Hoshea 2:13:

וְהִשְׁבַּתִּי, כָּל-מְשׂוֹשָׂהּ, חַגָּהּ, חָדְשָׁהּ וְשַׁבַּתָּהּ--וְכֹל, מוֹעֲדָהּ

It was probably overwritten by RJE, who took a Pasuk from J:

שֵׁשֶׁת יָמִים תַּעֲשֶׂה מַעֲשֶׂיךָ, וּבַיּוֹם הַשְּׁבִיעִי תִּשְׁבֹּת--לְמַעַן יָנוּחַ, שׁוֹרְךָ וַחֲמֹרֶךָ, וְיִנָּפֵשׁ בֶּן-אֲמָתְךָ, וְהַגֵּר

In fact, RJE seems to have copied a whole section of J into the law book of E (Shemot 23:12-19), presumably to make up for the text that had to be deleted.

We therefore conclude that the date of Rosh HaShana may well have been much older than P, and the same would or could be true for the date of Yom Kippur.