Giants aren't gonna do anything to spite the Jets, it's not that deep.
I'm not saying they won't trade up, but I don't see it as a given. Their GM (Gettleman) has never traded down in the 1st before, and has been on record saying "you can't get too cute with the draft". Meaning he's not gonna trade down if it means losing out on top tier prospects. That's why the Colts traded with the Jets and not the Bills, because they wanted to stay in the top 10, and their GM said the guy that they want will most likely still be available at 6 (I'm guessing Chubb).
Only team I could see the Giants trading with is Denver, and I'm not sure they're all that willing to trade up. MAYBE the Browns, but I doubt it.