I was going through the sources for early indo-iranian and according to B. Fortson the first documented manifestation of this branch are the proper names in Mitanni Texts. Since the indo-iranian word are very scarce in this documents and, if I understood it correctly, treated as prestigious borrowings, I wonder what is the base language of official papers of Mitanni Empire. I assume that Hurrian was the basic vernacular since the Hurrians stood for the core of the Empire's population, but I can only guess the language of the goverment. On the basis of the time and location I would say Akkadian but it's only an assumption. Does anybody has some solid information on this topic ?
The Mitanni texts are in Hurrian, a non-Indo-European and non-Semitic language. As you mentioned, they contain some loanwords and proper names taken from proto-Indo-Aryan. This form of Hurrian is written in an Akkadian-based cuneiform script, so it is likely that the scribes also used Akkadian for certain types of documents. By the way, "official papers" is not really the right term for a chancery that wrote not on paper but on clay.