I never knew Rubin designed the Def Jam logo. He did a really great job of it, IMO. As to
I wonder if def is "death" or def is like definitive?
Insofar as there is even a--ahem--definitive answer, I can provide some insight at least. In their paradigm-shifting 1984 book Subway Art, Henry Chalfont and Martha Cooper included a vocabulary page (p27) in an attempt for the wider audience to make sense of the then insular jargon used in the murals and graf-writer interviews they were presenting.
Def Really good (derived from "death").
I'll note that the graf community they were interviewing was obsessed with firsts, origins, and lore similar to how comic book nerds obsess over such details. Plus, Chalfont and Cooper actually hung out with these guys and knew writers from the early days from when these terms originated, so I consider it a pretty good source.
On the other hand, this is hip hop. MC traditionally meant master of ceremonies until a rapper with enough juice got everyone thinking of it as "microphone controller." At the time of this comic, def coulda meant both. It sure means both now, just ask El P.
As for Cookie Puss...