Nicely explained, Klingan! Kajanto, in his massive work The Latin Cognomina, gives CIL references for individual cognomina inscriptions. The first one I tried at the CIL site gave me "the normal answer" that you'd mentioned. I didn't see an accompanying ILS number, though.
My second attempt, on the cognomen "Crispio" yielded two "squeezes" and a bibliography reference:
Sayar, Mustafa Hamdi
Perinthos-Herakleia (Marmara ereglisi) und Umgebung. Geschichte, Testimonien, griechische und lateinische Inschriften.
Wien: Verlag der