I'm about 112% sure that a T-Mobile Note will not work on VZW... The reverse will work, VZW to TMO, but not the way you're going. You could unlock it legally with TMO by having service with them for 3 months (even prepaid) but most unlock companies can no longer get codes fromantic TMO due to the fact that so many people bailed on their payment plans and tried to take devices to other MVNOS and carriers.
I think the current policy is 2 months of post paid service or 3 months of prepaid. Either way, it's about $100 on the lower end to do it.