This is sort of my area of expertise at least with respect to Princess.
Chase has had my reservation since July and they can’t always refare it but I’ve been able to change rooms and get the new lower rate. When I first booked in June I booked an obstructed balcony room with the basic (Plus) package for $6,900. I’ve moved up three categories and upgraded my package and my current fare is $5,200. I haven’t used my urs to pay for it yet though. I would think you’d get a refund of urs (which will take months) but am not sure.
The other option with Princess is the better than best price guarantee form where they’ll give a credit that you can use for things like excursions.