The Chase cruise department can get you the price you see on NCL. There are only 2 reasons to book with NCL first
1. You want to pay part of the cost with a non UR earning CC
2. You want to delay spending your UR points
Do you want to do either of these things?
If you do then you would book with NCL, call Chase to get a
travel agent and their info (verify you can pay with UR at final payment, if that's what you're looking for), then request that NCL release the booking to Chase using their form which requires a TA name and phone number. It's simple, just not as simple as transferring over the phone. My reservation was transferred same day I submitted the form. You have 30 days from initial booking to transfer.
If you don't, just call up Chase and book through them. Tell them the cruise you're looking at and verify the price. Should be the same, if not tell them what you see and they should be able to find that.