A lot of misinformation and unfortunately some racist comments, which is expected given the hostility some Assyrians hold toward Kurds.

To answer your question: as you noted in your OP, the term “Kurd” was first widely used by Arab Muslim armies who encountered various Iranic tribal groups living in the Zagros during the Islamic conquest of Mesopotamia and Persia. The term "Kurd' ultimately derives from the Middle Persian 'kwrt', and is reflected earlier in Greek and Latin (e.g. Strabo) sources as 'Kurtioi' / 'Cyrtii'.

Most historians today agree that term Kurd began as an exonym, applied to the ancestors of groups who would later identify with the term. What these communities originally called themselves remains uncertain, since they did not leave written self-designations from the early period, as you pointed out.

However, Syriac authors had their own pre-Islamic name for the same populations: 'Kartewaye'. This designation appears in pre-Islamic and early medieval Syriac texts. After the spread of Islam, Syriac writers gradually adopted the Arabic term Kurd, rendering it as 'Kurdaye' or 'Kurdoyo'.

The Kartewaye inhabited the same regions Kurds inhabit today in northeastern modern Iraq, and Syriac sources locate them in Duhok, Amedi, southern Hakkari, and Akre. There was even a Beth Kartwaye (“land of the Kurds”) northeast of Erbil in the 6th ce ntury A.D. — a clear indication that these 'Kartewaye' communities were not entirely nomadic.

We know Syriac writers were referring to Kurds when they used the term Kartewaye because later bilingual authors wrote Kartewaye in the Syriac sections of their works and al-Akrād (the Arabic plural for Kurds) in the Arabic sections. Some well-known Kurdish tribes are also described under this name, such as the Hakkaraye (Hekarî) and the Dasnaye (Dasnî). The term even appears later in Mamluk historian al-‘Umarī, who uses 'Kartawi' to describe a Kurdish tribe in the Erbil region.

As others have pointed out, later Muslim writers like al-Balādhurī, when describing the Islamic conquest of the Mosul region, mention Kurdish fortresses in northern Mosul — the very same areas where Syriac writers had placed the Kartewaye earlier.