Well, I cleaned the old flyback, stuck it in, and THE CRACKLING WENT AWAY!!!
Unless I somehow screwed up putting the new one in, and then did a great job putting the old one back in, I am going to have to assume that my new flyback was bad

I doubt there would be any warranty on such a part, and furthermore, it's always possible that I did something wrong that caused it to go bad (don't know what). Wondering if I should take the new flyback somewhere to have tested, just to confirm it's bad (although it's probably not worth the cost for a $20 flyback).
Thanks to everyone who gave me input!