"But I'd swap the second amendment for a data privacy amendment in a heartbeat."
In practice, that would be a bad trade, because you can verify that you still have your 2A rights by being in possession of a gun, whereas with data privacy, all you have are solemn assurances that your rights are being respected, and when you discover you were lied to and you didn't actually have data privacy after all, you've got nothing.
If you mean some sort of impossibly-strong, enforced-by-God-or-aliens data privacy amendment, maybe. But that's not on the table.
(My point here is independent of the question of the 2A itself, but just looking at it as the proposed trade. Trading something concretely verifiable for promises that the promising people have every motivation to break secretly and you have no ability to audit is a bad trade.)