"Do you think we need to keep pushing back or risk overtightening?"

Yes.

Keep pushing back. It's ridiculous that they are not exchanging it right away. Who is the dealer?

If you purchased through a credit card, and the dealer continues to refuse to exchange the defective sink, dispute the charge with your credit card company; make sure you have pics to show them evidencing how the sink is out-of-level.

Thanks, they now said they contacted their rep for Karran so we’ll see what happens. Not happy with the foot dragging so far. We purchased through a local home store (try to support local businesses when possible). I attached a photo with a shim so you can see how large the gap is.

Send the sink back please.