Wait, wait! Assuming what is to be proved! I don't know that you're wrong, but I don't know that you're right either. I wouldn't make a big deal of this but it struck me that the notes in my NEB blithely assert that Peter is writing to Gentile Xtians, while my NAB -- the translation evidently done as a project by an English as a Second Language class -- In the Study bible version, (No pictures, though, darn it!) says,
Numerous allusions in the letter suggest that the churches addressed were largely of Gentile composition (1,14,18; 2,9-10;4,3-4), though considerable use is made of the Old Testament (1,24; 2,6-7.9-10.22;3, 10-12)I don't know why they punctuated the references that way. I just pray, pay, and obey. And I'm not saying they're necessarily right. I'm just saying it's not a slam-dunk that this was addressed to Jews.
But notice to whom it is addressed: "the sojourners scattered throughout Pontus, Galatia, Cappadocia, Asis, and Bithynia, Elect according to the foreknowledge of God" --- those are the Jews of the diaspora in northern Asia Minor.